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The Cambridge Technical Series
General Editor: P. Abbott, B.A.
ELEMENTARY PHYSICS
FOR ENGINEERS
CAMBRIDGE UNIVERSITY PRESS
C. F. CLAY, Manager
iLonHon: FETTER LANE, E.G.
enmburgt): loo PRINCES STREET
fitia lorfe: G. P. PUTNAM'S SONS
Bombag. Calcutta anH fSaUraB: MACMILLAN AND CO., Ltd.
Coronto: J. M. DENT AND SONS Ltd.
ffokBo: THE MARUZEN-KABUSHIKI-KAISHA
AH rights reserved
-\4
ELEMENTARY PHYSICS
FOR ENGINEERS
AN ELEMENTARY TEXT BOOK FOR FIRST
YEAR STUDENTS TAKING AN ENGINEERING
COURSE IN A TECHNICAL INSTITUTION
BY
J. PALEY YORKE
Head of the Physics and Electrical Engineering Department
at the London County Council School of Engineering
Poplar, London
Cambridge :
at the University Press
1916
PREFACE
THE importance of Physics to the engineer is in-
estimable but the student of engineering does
not often recognise the fact.
This little volume is intended to appeal to him
firstly because it is written specially for him and
secondly because the author has attempted to present
some essential facts of elementary physics as briefly
and straightforwardly as possible without any pedantry
or insistence upon details of no practical importance.
He has also avoided all reference to historical deter-
minations of physical constants and has described in
all cases the simplest and most direct methods, merely
indicating the directions in which refinements might
be made. At the same time he has endeavoured to
make no sacrifice of fundamental principle and no
attempt has been made to advance with insufficient
fines of communication.
The author frankly admits that he has tried to be
interesting and readable, and in case this should be
regarded as a deplorable lapse from the more generally
accepted standards he pleads the privilege of one who
has had considerable experience with students of engi-
neering in Technical Institutions.
He hopes by this little volume to induce a greater
number of engineering students to recognise that
Physics is as essential to engineering as is Fuel to a
Steam Engine.
J. P. Y.
London, 1916.
CONTENTS
CHAPTER I
MATTER AND ITS GENERAL PROPERTIES
Definition of matter. Weight. Force. Mass. Inertia. Theory
of structure of matter. Indestructibility of matter. Classifi-
calion of matter. Solids, liquids and gases. Density. Modes
of determination. Elasticity. Strain and stress. Hooke's
Law. Modulus of Elasticity . . . pages 1-14
CHAPTER II
PROPERTIES OF LIQUIDS
Pressure produced by liquids. Pressure at different depths. Upward
pressure. Pressure at a point. Pressure on sides of a vessel.
Buoyancy. Floating bodies. Archimedes' principle. Specific
gravity or Relative density and modes of determination.
Hydrometer. Pumps. Capillarity. Surface Tension. Diffusion.
Viscosity 15-36
CHAPTER III
PROPERTIES OF GASES
Weight. Pressure exerted equally in all directions. Atmospheric
pressure. The Barometer. The relationship between volume
and pressure 37-47
CHAPTER IV
FORCE, WORK AND ENERGY
Units of Length, Mass, Time and Volume on British and metric
systems. Force. Units of Force. Work and its measurement.
Examples on both systems. Energy. Potential and kinetic
energy. Various forms of energy. Principle of conservation
of energy. Power 48-56
Contents vii
CHAPTER V
HEAT AND TEMPERATURE
Production of heat. General effects. Distinction between Heat
and Temperature. Measurement of Temperature. Fixed
points. Construction and calibration of Mercury Ther-
mometers. Scales of Temperature. Other Thermometers.
Pyrometer. Self-registering Thermometers. Clinical Ther-
mometer 57-71
CHAPTER VI
EXPANSION OF SOLIDS
Laws of expansion. Coefficient of Unear expansion and mode of
determination. Some advantages and disadvantages of the
expansion of solids. Superficial expansion. Voluminal ex-
pansion . "^ . . 72-80
CHAPTER VII
EXPANSION OF LIQUIDS
Real and apparent expansion. Modes of determination of co-
efficients. Peculiar behaviour of water. Temperature af
maximum density 81-85
CHAPTER VIII
EXPANSION OF GASES
Charles' law and mode of experimental verification. Variation of
pressure with temperature. Absolute zero and absolute scale
of temperature 86—94
CHAPTER IX
MEASUREMENT OF HEAT
Units of heat on different systems and their relationship. Specific
heat. Water equivalent. Measurement of specific heat.
Calorific value of fuels. Mode of determination. Two values
for the specific heat of a gas .... 95-106
viii Contents
CHAPTER X
FUSION AND SOLIDIFICATION
Change of physical state by application or withdrawal of heat.
Melting and freezing point*'. Heat required to melt a solid.
Latent heat of fusion. Melting points by cooling. Change of
volume with change of state. Solution. Freezing mixtures.
Effect of pressure on the melting point . 107-114
CHAPTER XI
VAPORISATION
Vaporisation. Condensation. Evaporation. Ebullition. Boiling
point. Effect of pressure on boiling point. Temperature of
steam at different pressures. Heat necessary for vaporisation.
Vapour pressure. Boyle's law and vapour pressure. Tem-
perature and vapour pressure. Latent Heat of vaporisation.
Sensible Heat and Total Heat. Variation 6f Latent Heat of
steam with temperature. Pressure Volume and Temperature
of saturated steam. Hygrometry. The dew-point . 115-132
CHAPTER XII
TRANSMISSION OF HEAT
Conduction. Thermal conducti\'ity. Examples and appUcations
of conductivity. The safety lamp. Conduction in Uquids.
Convection in liquids. Hot water circulation. Convection in
gases. Ventilation and heating by convection. Radiation.
Reflexion and absorption of heat-energy. Transmission and
absorption of heat-energy. Radiation from different surfaces
at equal temperatures. Flame radiation. Dew formation.
133-148
CHAPTER Xm
THERM9-DYNAMICS
Mechanical equivalent of heat and mode of determination. Funda-
mental principle of the heat engine. Effect of compression and
expansion on saturated steam. Isothermal and adiabatic ex-
pansion. The indicator diagram .... 149-162
Index 163-165
CHAPTER I
MATTER AND ITS GENERAL PROPERTIES
We all know that there are many different states or
conditions of matter. Ice, water and steam are three
different conditions of exactly the same kind of matter ;
they differ only in having distinctive physical pro-
perties, being constitutionally or chemically identical.
Though they have certain distinctive characteristics —
such for example as the definite shape of a piece of ice
and the entire lack of shape of water or steam : the
definite volume of a given weight of water and the
indefiniteness of the volume of a given weight of steam
which can be compressed or expanded with ease — they
have nevertheless certain properties in common with
all other forms of matter.
Indeed it is common to define matter as that which
occupies space or that which has weight. Each of these
definitions names a property common to all matter.
It seems rather unnecessary to try to define matter :
we feel that everyone must know what matter is : and
the definitions are likely to introduce ideas more diffi-
cult to appreciate than the thing which is being defined.
But we can see nevertheless that it may be useful and
even necessary to have some definite dividing line
between matter and the various sensations which can
proceed from it. The colour of a rose is merely a
sensation : its perfume is the same : but the rose
p. Y. 1
2 Matter and its General ProperticH [CH.
itself is matter. Our distinction is that the rose lias
weight and occupies space. Colour has no weight, nor
does it occupy space.
Again when a piece of coal is burning it is giving
out Heat. Is that heat matter ? Well, if we ap})ly the
test of weight to it we find that it is not. A hot object
weighs neither more nor less than the same object
cold. If we weigh the coal before it is ignited and
then while it is burning if we collect all the products
of the burning — that is to say all the gas and smoke
and ash — we should find that there was no change in
weight. This is a well-known experiment — though
usually done with a piece of candle instead of coal —
and it is being mentioned now to shew that though this
burning matter is giving out heat, and also light, yet
these things are weightless and are therefore outside
our definition of matter. For if they had weight then
the mere residue of the ash and the fumes would not
have had the same weight as the original matter. We
will return presently to the further question of how we
shall classify Heat.
The experiment quoted above is one of many which
have led us to the firm belief that matter cannot be
destroyed. We can change its form both physically
and chemically but we cannot annihilate it. This is
one of the fundamental law* of physical chemistry and
one of the greatest importance and usefulness.
Weight. All forms of matter possess weight. It is
to be supposed that all readers know what is meant by
the statement. In books of this kind much space and
many words are used to convey to the readers' minds
ideas with which they must already be sufficiently
famiHar. W^e explain that Force is that which produces
i] flatter and its General Properties 3
or tends to produce motion : that it is also that which
is necessary to destroy motion : that it is also necessary
if the direction of motion of a body is to be changed.
We then proceed to define motion as the change of
position of a body with respect to some other body;
and we may even devote some space to the explanation
of what position is. It is extremely probable that
everyone knows these things, though it is very likely
that only a few could frame their knowledge in words.
In the same way weight is the attraction between
every portion of matter and the earth. This attraction
tends to draw everything vertically downwards towards
the earth. It is called the force of gravitation ; but
nobody has the least idea why the earth attracts things
or what this mysterious force is. We are so used to it,
it is so continiially present that we take it quite as a
matter of course, and never pause to consider that it
is mysterious and inexplicable. The attraction of a
needle to a magnet fills us with wonder or awe but the
attraction of a stone to the earth seems to be inevitable
and ordinary.
Weight then is a/orce ; it is a particular force which
acts only in one direction upon matter, and that
direction is vertically downwards. Of course the force
is also tending to pull the earth vertically upwards,
but the reader will have no difficulty in appreciating
the fact that no movement of the earth as a whole would
be detected by us. We can think of every portion of
matter being attached to the centre of the earth by
imaginary stretched elastic threads. These threads
will be in tension and will tend to shorten by pulling
the object and the earth towards each other. The pull
will be equal in both directions — but when we think
1—2
4 Matter and its (Sineral Properties [CH.
of the enormous mass of the earth compared with the
mass of the object we may be considering we can
readily see that the object will go downwards much
more than the earth will come up. At the same time
we can see the tendency and in seeing that we are also
seeing something of a very important mechanical law
about the reaction which accompanies every action.
We say then that matter is that which possesses
weight. Air and all other gases can be weighed by
taking a flask, exhausting the air from it by means of
a vacuum pump, weighing it carefully, and then
allowing either air or any other gas to enter it when
it can be weighed again. The increase in weight will
represent the weight of that flask of the gas at the
particular pressure under which the flask was filled.
If a higher pressure were used then, as more gas would
be forced into the flask, the increase in the weight would
be correspondingly greater.
Mass. This leads us naturally to the meaning of
the word mass. By the mass of a body we mean the
quantity of matter in it. This is often confused with
bulk or volume and of course the greater the volume
of any one particular kind of matter the greater must
be the quantity of that matter. But on the other
hand is there the same quantity of stuff in a cubic
foot of cork as there is in a cubic foot of lead ? Is there
the same quantity of steam in a given boiler, with the
water level at a certain point, whatever the steam
pressure may be? The answers will suggest that we
cannot compare the masses of different kinds of matter
by comparing their volumes.
It is usual to compare masses of matter by weighing
them. A quantity of cork weighing 1 pound contains
i] Matter and its General Properties 5
the same quantity of matter as a piece of lead weighing
1 pound. At the same time we must be careful to
remember that weight is simply the force of attraction
between the matter and the earth and that mass is the
quantity of stuff in it. When we ask for a pound of
sugar we want a mass of it which is attracted to the
earth with a force of 1 lb. weight.
It may help us to see this distinction if we remember
— as most of us probably do — that a given object has
slightly different weights or forces of attraction at
different parts of the earth, owing to the shape of the
earth and to the fact that at some places we are nearer
to its centre than at others. Well, although an object
may have different weights, yet we know that its mass
must remain the same. This helps us to see the dis-
tinction between the two — though it may suggest
certain difficulties in buying by weight from different
parts of the earth. As a matter of fact the difference
is very slight — about two parts in a thousand at the
outside — and if the substances be weighed with balances
and "weights" we can see that the "weights" will be
equally affected and that we should get equal masses
from different places. But if spring balances be used
then a pound weight of sugar sent from a place far
north would be a smaller mass than a pound sent from
a place near the equator.
The reader will learn in the mechanics portion of
his course of study how masses may be compared in
other ways in which the weights are eliminated.
Inertia. There is another property, called Inertia,
which is common to all forms of matter. When we
say that matter has inertia we mean {a) that it cannot
start to move without the application of some force.
() Matter and its General Properties [cH.
(6) that, if moving, it cannot stop without the appli-
cation of force, (c) that if moving in any particular
direction it will continue to move in that direction
unless some force or forces be applied to it to make
it change its direction. That is to nay force is necessary
to overcome inertia.
Inertia is not a cause and it is not a reason. It is
the name given to the fact that every object tends to
remain in whatever condition of motion or rest it may
be at any given moment. That tendency means that
it is very difficult to start'anything suddenly/ or to stop
it suddenly or to change its direction of motion suddenly.
Experimental verification of these truths may be ob-
tained by anyone during a short journey in a tramcar.
If one is standing in a stationary car, scorning the
friendly aid of "the strap," and the car starts abruptly
one learns that matter (oneself in this case) tends to
remain in its previous condition of rest, and that straps
are really useful adjuncts of the car.
If the motorman suddenly applies his brakes and
reduces the speed of the car the passengers shew a
unanimous tendency to continue their previous speed
by side-slipping along their seats in the direction of
the car's motion. If one is walking towards the con-
ductor's end during this slowing down process one finds
considerable difficulty in getting there, just as though
one was climbing a very steep hill against a stiff breeze.
If one is walking towards the motorman's end and he
slows down one finds it difficult not to run . In rounding
a sharp curve — that is'to say changing the direction of
motion — there is always the tendency to be thrown
towards the outside of the curve, shewing the tendency
of moving matter to continue in its original direction.
i] Matter and its General Properties 7
There are countless examples of tljis property of
matter. A hammer head reaches a nail, but it does not
stop suddenly : the distance the nail is driven in depends
on the kind of nail and the substance and the weight
and the speed of the hammer. Chiselling, forging,
pile-driving, wood-chopping, stone-breaking and cream-
separating are amongst the many processes which
depend upon the fact that matter possesses inertia.
The "banking" of railway tracks at all curves so that
the outer rail is higher than the inner is necessary to
assist the train to change its direction of motion.
When a motor car or a bicycle side-slips it is due to
the tendency to continue in its original direction and
if it is taken round the corner too sharply the result
will be side-slipping or overturning to the outside of
the curve. Most people fondly believe that if a cart
is taken too suddenly round a bend it will fall inwards.
Let the reader ask any half-dozen of his friends.
Then we know how difficult it is to start moving on
a very slippery floor, or on ice, and how equally difficult
it is to stop again. It is not suggested here that one's
inertia is any greater than it would be on a rough floor :
the point is that one cannot get a "grip" and thus
cannot exert such a large force either to start or to
stop. The skidding of a locomotive when starting
with a train of great mass is another example of this
point.
Theory of Structure of Matter. In order to explain
and connect the many facts of nature it is necessary
that we should have some idea of the structure of
matter. The generally accepted theory is that known
as the kinetic theory, a theory which assumes that all
substances are composed of an enormous number of
H M<itter and Its General Properties [ch.
very small particles or grains called molecules. Further
it assumes that these molecules are not generally in
contact with their neighbours but are in a state of
continued agitation and vibration ; that collisions
between them are of frequent occurrence ; that even
when any two or more are in contact with one another
there are distinct interspaces between them called
inter-molecular spaces.
According to this theory a portion of matter is not
continuous substance but a conglomeration of small
particles which attract one another with a force called
cohesion.
The motion of the molecules in solid matter is very
restricted : it is probably rather in the nature of
vibration or oscillation than migration. In liquids
the molecules are not supposed to be so close together
and thus may thread their way through the mass like
a person in a crowd. In the case of gases the spaces
between the molecules are assumed to be still greater
so that the molecules can move about with considerable
freedom.
It is also believed that the hotter a body is the
greater does the movement and vibration of each
molecule become. That is to say, the energy of move-
ment of each molecule is increased as the temperature
is increased. Indeed from this theory it is argued that
if the temperature could be lowered until there was no
molecular agitation there could be no heat in the body
and such a temperature would be the absolute zero of
temperature.
Classification of matter. Apart from the properties
which are common to all kinds of matter there are
other properties which are peculiar to one form or
i] Matter and its General Properties 9
another. Such properties enable us to classify matter
into different groups. In physics such classification is
based solely upon physical properties and our groups
are only three in number namely, solids, liquids and
gases. Sometimes indeed it is said that there are only
two groups, solids and fluids, the word fluid including
liquid and gas.
Solids are distinguished from fluids — that is from
liquids and gases — in that each portion of a solid has
a definite shape of its own. This property is termed
rigidity. Liquids and gases have no rigidity : a portion
of a hquid has no definite shape though it has a definite
volume : a given weight of a gas has no definite shape,
and its volume depends upon the pressure acting upon
it. This latter fact helps us to distinguish between
a liquid and a gas. A liquid is practically incom-
pressible but a gas is readily compressed.
A fluid cannot resist a stress unless it is supported
on all sides.
Density. Though all forms of matter have weight
yet if we take the same bulk or volume of different
forms such as cork, #ater, lead and marble we shall
find that they have different weights.
The mass of a unit volume of a substance is called
the density of that substance.
If we know the density of a substance we can
calculate either the mass of any known volume or the
volume of any known mass.
On the British system of units density would be
expressed in pounds per cubic foot. On the metric
system it is expressed in grammes per cubic centimetre.
Thus the density of pure water (at 4° C.) is 62-4
approximately on the British system and 1 on the
10 Matter and its General Properties [en.
metric system. I^ead is 705-12 on the British and 11-3
on the metric. Of course in both systems the lead
is 11-3 times as heavy as the same bulk of water.
(See Chapter II.)
For the determination of the density of a substance
it is only necessary to be able to weigh a portion of the
substance and then to find its volume. If the substance
has a regular form its volume can be calculated. If it
be irregular it can be immersed in water and the volume
of displaced water can then be measured. There are
many simple methods of obtaining and measuring the
displaced water. There is the obvious method of
placing a label to mark the level of water in a vessel
and then placing the substance in the vessel. The
water above the label mark is now sucked out by means
of a pipette until the level is restored. The volume of
the water removed must of course be that of the sub-
stance and it can be measured in a graduated vessel.
tA^
n
=^w
— , ,
'"
-1-
==.=^—
.-_— _
~-~
_-_— .
— -
(a)
a
W
^
Fig. 1
Fig. 1 illustrates special forms of vessels designed to
facilitate the collection and measurement of the dis-
placed water. In (a) the vessel i» filled up with water
and allowed to adjust its level through the side spout.
I]
Matter and its General Properties
11
A dry measuring vessel is then placed under the spout
and the substance whose volume is required is carefully
lowered into the water. The other form (6) is called a
volumenometer and it utilises a small siphon with the
ends drawn out to fine points. This prevents the
siphon from emptying itself. Its use is obvious.
More refined methods depend upon weighing instead
of measuring the displaced water (as with the specific
gravity bottle) and upon the principle of Archimedes.
The reader will be able to appreciate these after reading
Chapter II.
Densities of some common substances.
Substance
Density in lbs. per
cubic foot (approx.)
Density in grammes
per cubic centimetre *
Platinum
1344
21-522
Gold
1200
19-245
Lead
712
11-^
Silver
655
10-5
Copper
549-556
8-8 -8-9
Iron (wrought)
466-487
7-47-7-8
Iron (cast)
378-468
6-9 -7-5
Steel
435-493
7-73-7-9
Brass
505-527
8-1 -8-45
Oak
43-2-61-9
0-69 to 0-99
Water
62-4
1
* Since the mass of 1 cubic centimetre of water is 1 gramme it
follows that the density of a substance in grammes per cubic centi-
metre is numerically equal to its relative density or specific gravity
with respect to water (see page 25).
Properties of Solids. Different solids differ from
one another not only in chemical composition but
also in physical characteristics. Such properties of
solids as porosity, hai-dness, malleability, ductility,
12 Matter and its (itcueral Properties [CH.
plasticity and elasticity are shewn in various degrees
in different substances. The nature of the properties
denoted by the words above is generally understood —
with the exception, perhaps, of that property called
elasticity.
Elasticity. If the reader were asked to state what
was the most highly elastic substance we know of he
would probably give india-rubber without much
hesitation. Now elasticity is measured by the mag-
nitude of the force which is necessary to produce a
given change in the shape of a substance : and for such
comparison it is necessary that all the substances used
be of the same original dimensions. If we were going to
compare elasticity so far as stretching is concerned then
we would use wires of equal length and equal diameter
and we would find out what weights we should have to
load on the bottom end in order to stretch them by
the same amount. That substance which required the
largest weight would have the gTesii^st elasticity.
Of course it would be necessary to see that when
the weiglits were removed again the wires returned to
their original lengths. If they did not — that is if they
were permanently stretched — then we must have loaded
them beyond their limits of elasticity. Some substances
can be temporarily stretched to a great extent and such
are said to have wide limits of elasticity. Thus india-
rubber has not a very high degree of elasticity — that is
to say it is easily stretched — but it has very wide limits
of elasticity. Steel has a high degree of elasticity but
very narrow limits.
The same statements apply to compression, to
bending and to twisting.
Stress and Strain. When the form or shape of a
i] Matter and its General Properties 13
body has been altered by the apphcation of a force the
alteration is called a strain. If a piece of india-rubber
is stretched (from 6 inches to 7 inches) the change is
called a strain. The same term would be used if it
was compressed to 5 inches, or twisted round through
any number of degrees, or bent to form an arc. The
force producing the strain is called a stress. In strict
usage the word strain is used to denote the change
produced per unit of length. In a case of stretching
for example the extension per unit length of the sub-
stance is the strain. If a wire be 60 inches long and it
is extended by 1-5 inches then the strain is
Similarly stress is used to denote the force per unit
area of cross section. Thus if the wire quoted above
has a diameter of 0-05 inch and the stretching force
was 10 lbs. weight the stress would be 10 -^ area of
cross section of the wire
= 5095 lbs. per sq. inch.
3-14 X (-025)2
Hooke's Law. From a series of experiments Hooke
deduced the law that within the limits of elasticity the
extension of a substance is directly proportional to the
stretching force.
It may also be expressed that strain is directly
proportional to stress. The ratio of - — ^ for any
stram
substance is called Young's modulus for that substance.
This is an important quantity in that section of
engineering work dealing with the strength of materials.
Hooke's law also applies to twisting. If a wire be
^
11 Mutter and its (Icneral Projtcrticn [CH. i
rigidly fixed at one end and a twisting force applied
to the other the angle of twist or torsion will be directly
proportional to the twisting force. It also applies to
bending. If a beam be laid horis^ontally with each end
resting on a support and it be loaded with weights at
the centre it will bend. The extent to which the centre
of the beam is depressed vertically below its original
position is called the deflexion of the beam. The
deflexion is directly proportional to the bending force.
It will be obvious that in all these cases — stretching,
compressing, twisting or bending — the amount of change
produced will depend not only upon the force applied
but also upon the original length of the substance,
upon its cross sectional area and upon the particular
material used.
EXAMPLES
(See table above for densities)
1. What is the weight of a cyUnder of copper (a) in lbs., (b) in
grammes, if it is 6" high and 2" diameter and an inch is approxi-
mately 2"54 cms. ?
2. What would be the volume of a piece of gold which would
have the same weight as 1 cubic foot of silver?
3. If sheet lead costs £27 per ton, what will be the cost of a roll
32 feet long, 3 feet wide and J" thick ?
4. What is the density of the sphere which weighs 4 lbs. and has
a diameter of 3 inches ?
5. In what proportions should two liquids A and B be mixed so
that the mixture shall have a density of 1-2, the density of A being
0-8, that of 5 1-6.
6. A wire of diameter 0-035 inch and 6 feet long is found to
become longer by 0-25 inch when an extra weight of 14 lbs. is hung
on to it. What is the stress and the strain and Young's modulus
of elasticity ?
CHAPTER II
PROPERTIES OF LIQUIDS
As we have seen liquids have no rigidity and there-
fore have no definite shape. A given mass of Hquid
will always assume the shape of the portion of a vessel
which it occupies. Moreover a liquid is practically
incompressible and in this respect it differs from those
fluids which we call gases.
If we place some water in a vessel we know that the
weight of the water must be acting on the base of that
vessel. But we also know that the water does not
/
Fig. 2
merely exert a downward pressure. If holes are
pierced in the vessel at positions A and B — as shewn
in Fig. 2 — we find that the water streams out through
16 Properties of Llqukh [CH.
thoni aiul that it comes out from B with a greater
velocity than from A. This indicates firstly that the
wat«r must be exerting horizontal pressure on the sides
of the vessel : and secondly that the pressure at B is
greater than that at A .
Pressure at different depths. It does not require
any deep reasoning to realise that as we pour more water
into a given vessel the downward pressure upon its base
must increase and that the greater the depth of liquid
the greater will be this downward pressure.
If we did not conduct any investigations we might
be led to conclude that if we place a piece of cork
sufficiently- far below the surface of water it would
sink — forced downwards by the enormous pressure
which would be exerted at a great depth. But our
experiences — that is to say our investigations, whether
they were deliberate or casual — tell us that this is not
true. Our experiences tell us that when we put our
hands under water we are not conscious of an extra
weight upon them : that when w^e put them at greater
depths we are not conscious of any greater weight than
when they were near the surface : that, in fact, we are
conscious that our hands seem to be altogether lighter
^when held under the water and that different depths
do not appear to make any difference at all upon the
sensation of lightness. Our experiences teach us that
when we dive into water, instead of being weighed down
by the weight of water above us we are in fact buoyed
up and we ultimately come — at any rate those of us
who are reading must" always have come — to the
surface.
Well then, our experiences tell us that somehow or
other there appears to be an upward pressure in a
11]
Properties of Liquids
17
liquid. One simple experiment to illustrate this is to
take a piece of glass tube open at both ends ; close one
end by placing a finger over it ; place the tube vertically
in a tall jar of water with the open end downwards.
A little water will be forced up the tube — compressing
the air inside. As it is lowered further more water
will be forced up the tube and the air inside will
be more compressed. There must be some upward
pressure to do this. Then remove the finger from the
top : water will rush up the tube and may even be
forced out through the top in the first rush. Ultimately
it will settle down so that the water level inside the
tube is the same as that outside — suggesting therefore
that this upward pressure at the bottom of the tube is
exactly equal to the downward pressure there.
ILL
(a) (h)
Fig. 3
A more convincing experiment is illustrated by
Fig. 3. A fairly wide glass tube open at both ends
has one end carefully ground flat and a circular disc
1 }{ Properties of Liquids [CH.
of aluminium is placed against this end. It is held
tightly on by means of a piece of string passing up
through the middle of the tube. It is then immersed
in a tall jar of water — the disc-covered end downwards
— and it is found that the string is no longer necessary
to hold on the disc. The upward pressure on the bottom
of the disc is sufficient to hold it on.
If now some water be poured carefully into the tube
it will be found that the disc will not fall off until the
level of the water inside the tube is very nearly equal
to that in the jar. If the disc were made of a substance
of the same density as water it would hold on until the
level was quite up to that in the jar. This experi-
ment shews very clearly that the upward pressure on
the bottom of the disc was equal to the downward
pressure which would have been exerted on it if it had
been immersed at the same depth — for when the tube
was filled with water to the same depth as in the jar
we found that the downward pressure of this depth
just counter-balanced the upward pressure — making
due allowances for the weight of the disc.
In addition to this it can be shewn by a similar
experiment that the liquid exerts a horizontal pres-
sure and that the horizontal pressure is also equal
to the downward and the upward pressures : that in
fact at a given point in a liquid there is a pressure in
every direction and that it is equal in every direction.
Pressure at a point. It is necessary that we should
have some clear idea of what is meant by the pressure
at a given point in a Hjg[uid. If we consider the base
of a vessel, for example, it is clear that the weight of
water on the base depends not only upon the height of
water above it but also on the area of the base. And
ii] Prope7'ties of Liquids 19
since different vessels may have different base areas it
will be necessary for us in speaking of pressure at any
point to speak of the pressure per unit area at that point.
We may speak of the pressure per square foot or per
square inch or per square centimetre, and the total
pressure on any base will be the pressure per square
unit multiplied by the number of square units contained
in the base.
Let us suppose that we have a rectangular vessel
having a base area of 1 square foot and that it is filled
with water to a height of 1 foot. There is therefore
1 cubic foot of water weighing 1000 ozs. resting on a
square foot of base. Since there are 144 square inches
in the square foot the pressure per square inch must
be ^fff- = 6' 94 ozs. (approx.). We can say therefore
that the pressure at any point on that base area is
6-94 ozs. per square inch. And further whatever the
shape or size of the base may be if the water above it
is 1 foot high the pressure per square inch on the base
will be 6-94 ozs.
Pressure at a point depends only on vertical depth
and density. This last statement needs substantiation.
An experiment may be performed with a special U-tube
— shewn in Fig. 4 {a) — which is provided with a screw
collar at sc on which different shaped and sized limbs
may be screwed. Different limbs are shewn in (6), (c)
and (d). It is found that if water be poured into the
U-tube it will always rise to the same level on each side
whatever the shape or size of the limbs may be. Since
it follows that when the liquid comes to rest the pressure
exerted by the water in the two limbs must be equal,
therefore the pressure produced at a given point is
not dependent on the size or shape or quantity of water
2—2
i}(»
Properties of Li</ui{ls
[ni.
in I Ik- vrs.st'l hul only upon the verfical depth (see {(J))
of the point beh)\v the surface and u])on tlie density
of the liquid. Aiid it follows that if we have a number
of vessels having equal bases but having different shapes
and volumes the pressure on the bases will be equal
if they contain only the same vertical depth of the same
liquid. The explanation of this fact may not be very
obvious to the reader, but if he has any knowledge of
elementary mechanics he will know that there will be
"reaction^' at every point of the walls of the vessel.
If these walls be quite vertical as in (a), then the re-
actions will be horizontal and will balance one another,
but in the case of inclined walls the reactions, which
will be at right angles to the wall, will therefore add to
the mere water weight on the base in (c) whilst they will
counterbalance the extra water weight in the case (6).
Therefore in speaking of the pressure at a point in
a liquid we have only to think of the vertical depth of
that point and the density of the liquid. At a point
1 foot below the supface of water the pressure is
6*94 ozs. per sq. inch in every direction: at a point
L feet below it will be Z- x 6-94 ozs. per sq. inch. If
the liquid be D times as heavy as water bulk for bulk
II J Properties of Liquids 21
then the pressure at any point L feet below the surface
will be Z) X iy X 6-94 ozs. per square inch.
On the metric system it is even simpler because
1 cubic centimetre of water weighs 1 gramme. There-
fore the pressure per square centimetre at any point
below the surface will be D x L grammes, where
L = depth of the point in centimetres and D = the
number of times that the liquid is heavier than water.
On the metric system this D will be the density in
grammes per cubic centimetre.
Pressure on the sides of a vessel. Since at any given
point the pressure is equal in all directions it follows
that the pressure on the sides or walls of a vessel at any
point is determined in exactly the same way as it would
be for a point on a horizontal surface at the same depth.
But of course it will be seen that the pressure on the
walls increases gradually with the depth and that the
total pressure on the side can only be found by deter-
mining the pressure on each unit area and adding them
all together.
If the vessel has rectangular sides then we can get
the total pressure very simply by finding the pressure
at a point half-way down from the surface of the liquid
to the bottom and multiplying this by the total number
of square inches (or cms., according to units used) which
are under the water.
For example, in the case of the tank shewn in Fig. 5,
which is a cubical tank of 6 foot side filled to a depth
of 5 feet with water, the average pressure on one
side will be the pressure at a depth of 2-5 feet below
the surface. This is 2-5 x 6-94 ozs. per square inch
which is 17-35 ozs. per square inch. There are
5 X 6 = 30 square feet below the water and since
22
Properties of Liquids
[CH.
there are 144 square inches to the square foot it follows
that the total pressure on the side will be
144 X 30 X 17-35 ozs. = 74952 ozs. = 40845 lbs.
The total pressure on the base will be
(5 X 6-94) X 6 X 6 X 144= 179,885 ozs.
Fig. 6
In the same way the total pressure on a lock gate
would be calculated though in that case there would
be some water on both sides of the gate at the lower
portion. Further, though we get the total pressure in
this way it is not of much use in designing a lock gate
since it is necessary to design it to stand a much greater
pressure at the bottom than at the top of the gate.
The same applies to water tanks of any appreciable
depth — such as a ship's ballast tanks which are strength-
ened towards the bottom.
Buoyancy. If we imagine that a substance is placed
under water, as shewn in Fig. 6, we can see that the
water will exert upon it pressure in every direction.
But since the substance occupies space it is not a point
and therefore the pressure in every direction will not
be equal. On the upper surface A the downward
pressure will be due to the vertical depth 8 A ; whilst
on the lower surface the upward pressure will be due
n]
Properties of Liquids
23
to the vertical depth SB, and the side pressures will
balance one another. Thus we find that the upward
pressure is greater than the downward pressure.
Whether it will sink or float depends now upon the
weight of the substance. If this weight is greater than
the difference of . the upward and downward water
pressures then the substance will sink : but if its weight
is less than the difference between the upward and
downward pressures it will rise to the surface and float.
D
o
' '/ "
U
*? —
\'
-A—
B"-
ifference
UP
\
'm
/
^Bf
- ~ -
Is'
Fig. 6
This will be true whatever the liquid may be, but of
course the difference between the upward and down-
ward pressures will be different if we use liquids of
different density, and thus substances which would
sink in one liquid might float in another.
Floating Bodies. When a body floats so that the
top of it is above the surface then there is no down-
ward liquid pressure upon it at all. Therefore it will
float to such a depth that the upward liquid pressure
upon it is just equal to its own weight. If, therefore.
24
Properties of I/iqukls
[CH.
we take some similarly shaped pieces of different sub-
stances which will float, and put them on water the
denser substances will sink deeper than the lighter, and
the volumes of the submerged portions will be in pro-
portion to the densities of the several substances.
Archimedes' experiment. Figure 7 (a) represents a
spring balance on the hook of which is suspended a
hollow cyhnder or bucket. Under tliis is also suspended
a soUd cylinder having the same external dimensions
as the internal dimensions of the bucket and having
therefore the same volume. It does not matter what
this solid cyhnder is made of provided that it will sink
in water. The reading of J;he spring balance is shewn.
The solid cyhnder is then immersed in water — (6) —
and of course the arrangement weighs less than before
as shewn by the balance. The bucket is then gradually
II ] - Properties of Liquids 25
filled with water. When it is quite full (c) the balance is
found to shew the same weight as it did originally.
This is known as Archimedes' experiment and it
shews that the cylinder weighed less in water than in
air by the weight of its own volume of water.
If the experiment be repeated using some other
liquid it will be found that when the bucket is filled
with that liquid the original weight will be registered
on the balance.
Thus it is said that when a body is immersed in any
liquid its net weight is less than its weight in air by
the weight of the liquid which it displaces.
This is equivalent to saying that the difference
between the downward and the upward pressures on
an immersed body is equal to the weight of the liquid
which the body displaces. When the body is wholly
immersed the volume of displaced liquid is equal to
the volume of the body.
In speaking of a ship's weight it is customary to
state that its "displacement" is so many tons — a state-
ment which means that the volume of the water which
is displaced by the vessel when floating to its "no cargo"
line would weigh that number of tons. This, of course,
means that the ship and its fittings also have that weight.
Determination of Specific Gravity or Relative Density.
The specific gravity of a substance — which is the ratio
of the weight of any given volume of the substance to the
weight of the same volume of water — may be determined
in many ways. The direct methods consist simply in
weighing the substance and then weighing an equal bulk
of water. It is not always simple to find the volume of
the substance — though this can always be done "by
displacement," that is by immersing the substance in a
20 Properties of Liquida [ch.
graduated vessel ot water and noting the level of the
water before and after the substance is immersed. The
difference in the two volumes \v\\\ be the volume of the
substance and such a volume of water can then be
weighed. If the substance is one which dissolves in
watesr — like copper sulphate crystals for example — then
it can be placed in the graduated vessel containing some
liquid in which it does not dissolve — such as alcohol in
the case chosen. The difference in volume will give the
volume of the crystals and an equal volume of water
can then be weighed out.
The specific gravity or relative density as it is often
called is the ratio
Weight of a given volume of the substance
Weight of an equal volume of water
The reader will doubtless have many opportunities
of making this kind of measurement and it should be
unnecessary to give any details in these pages.
It should be pointed out however that these direct
methods may not give very accurate results owing to
the errors likely to arise in the volume measurements —
especially when such volumes are small. Thus it is
more usual to determine relative densities by utilising
the principle of Archimedes. If a substance be weighed
firstly in air and secondly suspended in a vessel of
water — as shewn in Fig. 8 — the difference between
these weights represents the weight of the same volume
of water as the substance. Thus the specific gravity
or relative density can be determined at once : and it
will be recognised that the weighing can be done with
great accuracy and that the w^hole measurement will
take less time than a "direct" method.
ii] Projyerties of Liquids 27
If the substance is one which floats in water, then,
after weighing it in air, a "sinker," of lead say, can be
attached to it and a second weighing done with the
sinker under water and the substance in air : then a
third weighing with both sinker and substance under
water. The difference between the second and third
weighings will be the weight of a volume of water of
the same bulk as the substance.
Fig. 8
The relative density of a Uquid is determined by
weighing a solid in air, then in water and thirdly in the
liquid. The difference between the first and second
weighings is the weight of a volume of water equal to
the volume of the substance ; and the difference be-
tween the first and third weighings is the weight of the
same volume of the liquid.
The relative density of a sohd soluble in water is
found by weighing in air and then in a liquid in which
it is not soluble. The specific gravity or relative
density of this liquid must be known or found. The
difference between the weighings is the weight of a
volume of liquid equal to the volume of the solid.
The weight of the same volume of water may then be
28
Properties of Liquids
[CH.
calculated since the relative density of the li((uid is
known. From this the relative density of the soluble
substance is found.
In the case of powdered substances like chalk or
sand the "specific gravity bottle" is used. This is a
bottle having a ground glass stopper through which
a fine hole is bored. The bottle is filled with water.
When the stopper is put in the excess is forced out
through the hole and thus the bottle may be com-
pletely filled. It is then weighed. The powdered
substance is weighed and then put into the bottle. It
displaces its own bulk of water. The bottle is weighed
again. The specific gravity of the powder can readily
be obtained from these weighings.
The Hydrometer. The hydrometer is a simple
device for measuring directly the specific gravity of
a liquid. It is made of glass and usually in the form
shcAvn in Fig. 9. It floats in an upright position and
the thin neck has a scale on it which indicates the
specific gravity of the fiquid in which it is floating. It
will always float to such a depth that the weight of the
ii] Properties of Liquids 29
liquid which it displaces will be equal to its own weight.
Thus in a lighter liquid it will sink further than in a
heavier liquid. In the figure (a) represents the position
in water, (6) in alcohol, and (c) in battery strength
sulphuric acid. It is usual to have a set of hydrometers
to cover a wide range of specific gravities.
Hydrometers are used in many different branches of
commerce and the "scales" are usually designed to
meet the particular cases. They are not usually direct
reading in terms of specific gravity but in terms which
meet the needs of the persons who use them. The
sailor's hydrometer for example simply indicates the
number of ounces above 1000 which will be the weight-
of 1 cubic foot of sea water. If the hydrometer sinks
to 25 it means that 1 cubic foot of that water will weigh
1025 ounces. The brewer's hydrometer has a scale
which is used in conjunction with a specially compiled
set of tables. And even some of the ordinary hydro-
meters have scales which require the use of some
constant or some empirical formula in order to obtain
the specific gravity of the liquid in which they are
immersed. Of such kinds perhaps Beaume's and
Twaddell's are best known.
Pumps. The action of the simple pumps should not
require any detailed explanation after the foregoing
discussions. The diagrams shewn should be nearly
sufficient.
Fig. 10 illustrates a simple lift pump. In the pump
a piston B can be moved up and down in a cylinder.
In the base of the cylinder is a valve — shewn in the
diagram as a flap — which will open if the pressure below
is greater than that above and shut if it is less. In the
piston 5 is a similar valve which opens and shuts under
;}()
Properties of Liiiuuh
[CH.
similar conditions. The cylinder base is connected to
the wat«r through a fall pipe.
When the piston is raised the effect is to expand
the air between A and B and so lower the pressure
there. This shuts the valve in B and the water from
the well is forced up the pipe P by the excess of the
atmospheric pressure over the cylinder pressure. Thus
the cyhnder becomes filled. The piston is then pushed
down. This sliuts the valve A and opens B so that
Fig. 10
Fig. 11
the water is forced to the top of the piston. The piston
is raised again and with it, of course, the water above it
which comes out of the outlet O. At the same time the
previous action is going on below the piston.
Fig. 1 1 illustrates a force pump in which the water is
forced out of the outlet under pressure. This is the tj^pe
of pump used for fire-engine work, garden pumps, etc.
ii] Properties of Liquids 3 1
The piston B has no valve. When it is Hfted valve
A is opened and C is closed. Water enters the pump
cylinder. On the downward stroke A is closed and the
water is forced through C into the chamber F. As the
water rises in this chamber above the lower level of the
outlet pipe it will compress the air until ultimately the
pressure will be sufficient to force the water through 0
in a more or less continuous stream.
It should be remembered that since pressure is dis-
tributed equally in every direction in a liquid a force
pump having a small cylinder can nevertheless be used
to produce a total enormous pressure. For example if
a steam boiler is to be tested for pressure, the test
employed is a "water test" in which the boiler is filled
completely with water. A hand pump capable of
generating 300 lbs. per sq. inch pressure is then coupled
to the boiler and the pump is operated. This pressure
is communicated to the boiler and the water will exert
an outward pressure of 300 lbs. per sq. inch on every
square inch of the boiler. Any leak will shew itself:
and in the event of the boiler breaking down no
hurt is likely to be caused to those conducting the
test.
It is in the same way that the hydraulic press,
the hydraulic ram and hydraulic jack are operated.
The reader possibly knows that the feed water
pump of a steam boiler pumps water into the boiler
against the steam pressure. If the steam pressure is
150 lbs. per sq. inch then the feed water must be
pumped in at a greater pressure. This can be done
with quite small pumps, for the pressure which can
be generated and distributed does not depend upon
the capacity of the cylinder.
32 Properties of Lltjuids [cji.
Capillarity. If we examine the surface of water in
a glass vessel we notice that all round the edge next
to the glass the water is curved upwards. If we dip
a piece of clean glass tube into the water we notice
the same curving against the wall of the tube both
inside and outside. If the tube has a fine bore we also
notice — perhaps to our surprise — that the water rises
inside this tube to a greater height than the water
outside. If we use tubes of different internal diameters
we shall find that the water rises to a greater height in
the fine bored tubes than in the large bores. Because
of this fact — that the phenomenon is shewn best with
tubes as fine as hairs — it is called capillarity.
If we use mercury instead of water we observe a
reversed formation of the surface, and the mercury in
the tube will be depressed below the surface of that
outside. Again as We use finer and finer tubes
the depression wiU become correspondingly greater.
Fig. 12 illustrates the surface formations in the two
cases. Fig. 13 shews what happens when these liquids
are poured into U -tubes having a thick and a thin
limb — the thin limb being a capillary tube^.
Mercury does not "wet" glass and if any hquid be
placed in a vessel of material which it does not wet its
surface would be formed similarly to the mercury in
glass. If a pencil of paraffin wax be dipped into water
it will be found that the edge of the water against the
wax is turned down. If a piece of clean zinc be dipped
into mercury the edge_of the mercury near to the zinc
will be curved upwards — just like water against glass.
There are many illustrations of capillary action.
' The size of the capillary tube is exaggerated for the purpose of the
diagram.
ii] Properties of Liquids 33
There is the feeding of a lamp -flame with oil : the
wetting of a whole towel when one end is left in
Water Mercury
Fig. 12
water : the absorption of ink by blotting paper : the
absorption of water by wood and the consequent
swelling of the wood.
Water Mercury
Fig. 13
Surface Tension. The surface of any liquid acts
more or less like a stretched membrane. A needle can
be floated on water if it first be rested on a cigarette
P.Y. 3
34 Properties of Liquids [CH.
paper which N\ill ultimately sink, leaving the needle
resting in a little depression on the surface — but
actually not making any contact with the water.
Many insects walk on the surface of water. A camel-
hair brush under water has its hairs projecting in all
directions, but when it is withdrawn all the hairs are
drawn together as though they were in a fine india-
rubber sheath. The formation of a drop of water
shews the same thing — how the water seems to be
held in a flexible skin. This skin is under tension and
endeavouring to contract. Hence we find rain drops
are spherical : drops of water run off a duck's back
like hailstones off an umbrella: lead shot is made by
"raining" molten lead from the top of a tall tower into
a water vat at the bottom.
Different liquids have different surface tensions which
can be determined or compared either by observing
the heights to which they rise in capillary tubes of
equal diameter, allowances being made for the different
densities of the liquids, or by a direct weighing method.
This consists in suspending a thin plate of glass vertically
from one arm of a balance and adjusting the balance.
A vessel of water is then placed beneath the glass and
gradually raised until the water just touches the lower
edge — when the surface tension pulls down the balance.
Weights are placed on the other pan until the glass is
brought up again so that its lower edge just touches the
water or whatever Uquid is being tested.
Diffusion. If we place some coloured salt solution
at the bottom of a vessel of water — and we can do it
very easily by means of a pipette — we shall find quite
a sharp dividing line between the heavier salt solution
and the lighter water. But if we leave them undisturbed
ii] Properties of Liquids 35
we shall find that very gradually some of the heavy
liquid will have come to the top and some of the
lighter water will have gone to the bottom and that
eventually the Kquids will become mixed. This
gradual intermingling — done apparently against the
laws of gravity — is called dijfusion.
Diffusion takes place more readily between gases
than between liquids, and every gas can diffuse into
every other gas : this cannot be said of Uquids.
In the case of gases it is impossible to keep them
separated one upon another — like oil upon water. This
is fortunate for us, because if gases arranged themselves
layer upon layer with the heaviest at the bottom and
the lightest at the top our atmosphere would consist of
successive layers of carbonic acid gas, oxygen, nitrogen,
water vapour and ammonia. Animal life would be
impossible. As it is however gases diffuse so readily
that they are all intimately mixed — and even in the
immediate neighbourhood of an oxygen manufactory
which takes its oxygen from the atmosphere there is
no sign of a scarcity of oxygen; this is due to the
rapid diffusion which takes place.
Viscosity. Some liquids are more viscous than
others. It is easier to swallow water than castor oil,
not so much because of any special or objectionable
flavour but because of the slow dehberate manner in
which the oil trickles down the gullet. The oil is said
to be viscous ; and treacle, honey and thick oils have
this property of viscosity to a great degree. It may
be said to be due to frictional forces between adjacent
layers.
Liquids which flow readily — like water or alcohol or
petrol — are called mobile liquids.
3—2
30 Proper ticK of Liquids [oh. ii
The viscosity of a liquid is usually lowered by an
increase in temperature : so much so that when super-
heated steam is used in a steam engine the question
of lubrication becomes more difficult.
Viscosity of different liquids may be compared by
finding the rate at which they may be discharged
through equal tubes under equal pressures.
EXAMPLES
1. What is the total pressure on the base of a rectangular tank
full of water, the internal dimensions being 6' deep, 8' long and
4' wide? Also find the total pressure and the average pressure
in lbs. per square inch on each side of the tank.
2. A diver is at a mean depth of 30 feet below the surface of
the sea. What must be the least pressure of the air supplied to him
in lbs. per square inch so that he does not feel the pressure of the
water upon his diving suit? The relative density of sea water is
1025.
3. A substance weighs 256 grammes in air and its relative
density or specific gravity is 8-4. What would it weigh if immersed
in water ? What would it weigh in a liquid of specific gravity 1-25 ?
4. A substance weighs 7-6 ozs. in air and 6-95 ozs. in water.
What is its specific gravity ? What is its volume in cubic inches ?
5. A substance weighs 32-6 grammes in air and 26 grammes in
a liquid whose specific gravity is 0-84. What is the specific gravity
of the substance and what is its volume ?
6. Four lbs. of cork of specific gravity 0-18 are securely fastened
to 15 lbs. of lead of specific gravity 11-4. Will they sink or float
when immersed in water ?
CHAPTER III
PROPERTIES OF GASES
As we have already seen a gas is a portion of matter
which has no rigidity and which is readily compressed.
It has neither definite shape nor definite volume, for
a given mass of it may be made to occupy various
volumes at will by varying the pressure to which it is
subjected.
We have already seen that gases have weight and
it is the weight of the air surrounding the earth which
causes the pressure commonly called the atmospheric
pressure. It is that same weight which causes the air
to hang round the earth instead of distributing itself
through the vast vacuous spaces which nature is said
to abhor. As the reader probably knows, the belt of
air about the earth does not extend to the moon — as
was supposed to be the case in the early part of the
seventeenth century— but is only a few miles deep.
,The total weight of this belt of air on the earth's surface
is enormous, and if the reader would like to know
exactly how much it is he can calculate it from the fact
that the pressure of the air is, on the average, 14* 7 lbs.
to the square inch. He has therefore only to calculate
the number of square inches on the surface of the earth
and multiply this by 14-7 and he will have the total
weight of the air in pounds.
When a gas is enclosed in any space it exerts pressure
iMi Properties of GascH [c'H.
ill every direction. Moreover it exerts pressure equally
in every direction. One of the simplest illustrations
which can be offered of the truth of this stat-ement is
that of the soap bubble. It matters not how we blow
into the bubble, or what manner of pipe we use, the
bubble is beautifully spherical. If the pressure of the
gas both inside and outside the soap film were not equal
in every direction then clearly the bubble' would not be
spherical in form.
If we construct a cylinder — as shewn diagiammati-
cally in Fig. 14 — and provide it" with a number of
pressure gauges, then when a piston is forced into the
Fig. 14
cylinder it will be seen that all the gauges indicate the
same pressure at a given moment. On the other hand
we know that if the cyhnder were filled with a solid —
like steel for example — and pressure was applied to the
piston there would be no pressure exerted on the sides
of the cylinder: it would only be exerted on the end.
If we filled the cylinder with water we should find that
it exerted pressure in all directions equally.
The fact that a gas exerts pressure equally in all
directions accounts for our unconsciousness of the
existence of atmospheric pressure. It would be im-
possible for us to hold our arms out at length if the
in] Properties of Gases 39
atmospheric pressure of 14-7 lbs. per square inch were
only acting downwards. The air would indeed be a
burden to us.
A simple experiment illustrating the magnitude of
this pressure may be made by exhausting the air from
the inside of a tin can. The surest and simplest way
of doing this is to put a little water inside the can and
boil it. When steam is coming freely from the opening
remove the flame, cork up the can, and plunge it
into a vessel of cold water. The can will immediately
collapse. The explanation is that the air was driven
out of the can by the steam, and that the cold water
condensed the steam thus reducing the pressure inside
the can to practically nothing. The pressure of the
air outside acting in every direction upon the can is
sufficient to crush it. It is probably known to many
readers how in certain engineering operations — tunnel-
ling under a river for example— the workmen work in
a high pressure space in a special "shield." The
pressure of the air in this shield is considerably higher
than that of the atmosphere outside and the men have
to pass through a sort of air lock in which the pressure
is gradually raised to that inside the shield or gradually
lowered to that of the atmosphere according to the
direction in which the men are going. The change of
pressure is decidedly unpleasant unless it is done very
gradually so that the pressure inside the body may never
differ sensibly from that outside.
It is well known that if a piece of paper be placed
over the top of a tumbler filled with water the whole
may be held in an inverted position and the water will
not force the paper away. In this case the downward
pressure on the paper is represented by the weight of
4()
Properties of Gases
[CH.
the water iji the tumbler and the upward pressure is
the atmospheric pressure of 14-7 lbs. to the square inch.
There is no downward atmospheric pressure on the
paper because there is no air in the tumbler. Unless
the tumbler be 34 feet or more in length the upward
atmospheric pressure will be greater than the downward
pressure of the water in th(> tuniV)ler : hoiu-(^ it will not
run out.
If a glass tube of about 3G inches length be arranged
as shewn in Fig. 15 so that one end dips under some
mercury and the other end is connected to a vacuum
To Vacuum pump
Pig. 15
pump the mercury will rise in the tube as the vacuum
improves until finally it reaches about 30 inches above
the mercury in the lower vessel. Beyond this it will
not rise however good the vacuum may be. If the
experiment be repeated with other liquids — and in
such a case the tube should be 40 feet long — it will be
found that water will rise to about 34 feet, glycerine to
about 30 feet, and so on. But in every case the height
to which the liquid rises will be such that it will produce
IIIJ
Properties of Gases
41
a pressure of about 14-7 lbs. per square inch at the
bottom of the cohimn — which is to say that the Hquid
will rise up to such a height that it produces a down-
ward pressure equal to that of the atmosphere.
The Barometer. It is on this principle that we
usually measure atmospheric pressure, the instrument
used being called a barometer. To construct a barometer
a glass tube of 36 inches length having a fairly thick
wall and a bore of about | inch is sealed at one end
and filled with clean mercury. Care must be taken
that no air bubbles or water vapour are left in ; and
to this end the tube should be thoroughly cleaned and
dried before filling. A finger is then placed over the
end and the tube is inverted and its lower end placed
in a dish or cistern of mercury. The finger is then
removed and the mercury will fall a little in the tube —
as shewn in Fig. 16 (a). Since there is no air in the
Fig. 16
tube the column of mercury will adjust itself to such a
height that its downward pressure is the same as that
of the atmosphere. The "height" of the barometer
42 Properties of Gases [v\\.
is the vertical difference of level between the mercury
in the tube and the mercury in the cistern. If the
tube be tilted as shewn in Fig. 16 (6) or made in the form
shewn in Fig. 16 (c) the mercury will adjust itself so that
the vertical difference of level is the same as in the
straight vertical tube.
Standard Barometer. In the usual standard pattern
of mercury barometer the cistern is provided with a
plunger, worked by means of a screw, which can be
adjusted so that the level of the mercury in the cistern
coincides with the zero mark of the scale of inches and
centimetres. This adjustment must always be made
before the height of the barometer is read. It will
be clear that unless some arrangement of this kind
is provided a rise in the barometer will draw some
mercury out of the cistern and the level vdW be below
the zero of the scale ; whilst a fall in the mercury will
raise the cistern level above the zero of the scale. In
the usual domestic pattern this is compensated for in
the marking of the scale : and it will be found that the
distances marked off are shghtly less than true inches.
It is of course cheaper to do this than to provide a
special cistern.
Boyle's Law. The relationship between the volvmae
which a given mass of a gas occupies and the pressure
to which it is subjected is expressed in a law known as
Boyle's law. This states that the volume of a given mass
of a gas, kept at constant temperature, varies inversely as
the pressure to which it is subjected.
Most of us learned jgomething about this law when
we played with popguns. We learned -that as we
decreased the volume of the air in the barrel of the gun
by pushing in the plunger we increased the pressure on
Ill
Properties of Gases
43
the cork and on the plunger until finally the cork was
blown out. We found that the plunger was harder
to push as it got further into the barrel and in learning
this we had got the main idea of Boyle's law, that if
we increase pressure we decrease volume. What we
had not learnt was the exact relationship between the
two, namely that the one varies inversely as the other.
Thus if the pressure be doubled the volume will be
halved : if the pressure be increased seven times the
volume will be reduced to one-seventh and so on.
This law may be experimentally verified by means
of the apparatus shewn in Fig. 17, in which we have
/\
I
Fig. 17
two tubes L and R connected by some rubber tubing.
L is sealed at the top and is graduated in cubic centi-
metres or inches or any other scale of volume. R is
44 Proper tHx of Goscs [CH.
open to the atmosphere and is arranged so that it can
be raised or lowered. A certain volume of dry air (or
any other dry gas) is enclosed in L by means of mercury
and the volume can be read off on the scale. By
raising or lowering R the pressure and volume of the
gas in L can be changed.
If the side R be adjusted so that the level of the
mercury is the same in both tubes then it follows that
the pressure is the same also. But the pressure on the
surface of the mercury in R is the atmospheric pressure
and therefore if we read the height of the barometer
we know the pressure of the gas in L and we can read
the volume on the volume scale. If R be now raised,
as shewn in the top diagram on the right, so that the
level of its mercury is above the level of the mercury
in the tube L, then it follows that the pressure of the
gas in L is greater than the atmospheric pressure by
the pressure represented by a column of mercury of
length AB — since it can support this column of mercury
in addition to the atmospheric pressiire. Therefore the
new pressure is the atmospheric pressure in inches or
cms. plus the difference in the level of the mercury in the
two limbs also in inches or cms. as the case may be. If,
on the other hand, the limb R be lowered so that its
mercury is below that in L it follows now that the
atmospheric pressure is greater than that in L by an
amount represented by the difference in level AB, so
that the pressure of the gas in L is the atmospheric
pressure minus the difference in level AB.
The following are some results obtained with this
apparatus :
Ill]
Properdes qf Gases
45
Volume
Heiglit of
Difference of
1 Pressure of
.Pres-
of gas
barometer
level AB
gas in L in cms.
sure X
in L
in cms.
in cms.
of mercury
Volume
8
75-8
+ 53
128-8
1030
11
75-8
+ 17-7
93-5
1028
12
75-8
+ 9-6
i 85-4
1024
15
75-8
- 71
68-7
1030
16
75-8
- 11-4
64-4
1030
17
75-8
- 15-2
60-6
1030
18
75-8
- 18-4
57-4
1033
24
75-8
- 32-8
43
1032
In the last column of the tabulated results the
product of the pressure and the volume is given and
it is seen that this product is practically the same right
down the column. When one quantity varies inversely
as another and a number of results are taken under
equal conditions then it will always be found that the
product of the two quantities is constant.
If Pj represents the pressure when the volume is
Fi and P^ represents it when the volume is Fg then
Boyle's law may be expressed
V, Pi-
That is to say the ratio of the volumes is equal to
the inverse of the ratio of the pressures under equal
circumstances.
Therefore ^i^i==^2^2-
Hence the fact that our last column is practically
constant js an experimental verification of the law.
The relationship between the volume and pressure
may also be plotted as a graph. Fig. 18 shews the
graph given by the results above. The form of
this curve is known mathematically as a rectangular
hyperbola.
40
Properties of Gases
[CH.
It will be seen later that Boyle's law is not universally
true, though for dry gases it can be regarded as suffi-
ciently true for all practical purposes.
25
20
15
10
5
1
X
50
150
200
Fig. 18.
100
Pressure
Curve shewing relation of volume and pressure of air
at constant temperature.
Airships. The principle of Archimedes is as true
for gases as it is for liquids. Any object weighs less
in air than it would do in a vacuum by the weight of
its own volume of air.' It also weighs less near to the
ground where the air is dense than it would do at a
higher level.
Ill] Properties of Gases 47
A balloon or any other lighter-than-air ship is filled
with a gas lighter than air and is made of such a volume
that the weight of air which it displaces is greater than
its own weight. It is thus buoyed up and will rise to
a height such that the weight of air displaced at that
height is equal to weight of airship and contents. To
ascend the volume of air displaced must either be in-
creased (as in the Zeppelin type) or the weight must be
decreased by dropping ballast. To descend the volume
of air displaced must be decreased.
EXAMPLES
1. A certain mass of aii- has a volume of 12 cubic feet when
there is a pressure of 14-7 lbs. per square inch (1 atmosphere) acting
upon it: what will its volume be when the pressure is [a) 10 lbs.,
{h) 17-5 lbs. per square inch?
2. A steel oxygen cylinder has an internal volume of 3 cubic
feet. It is filled with oxygen at a pressure of 120 lbs. per square
inch. What would be the volume of the gas at atmospheric pressure ?
3. If a mercury barometer reading was 29-4 inches, what would
be the reading of a glycerine barometer at the same time- — the
specific gravity of glycerine being 1-21 and that of mercury 13-6?
4. Plot the graph shewn in Fig. 18 and extend it on each side
to shew the volume changes between the pressures of 20 and 200.
5. A balloon on the ground where the atmospheric pressure is
14-7 lbs. per square inch displaces 30,000 cubic feet of air. What
volume will it displace when at such a height that the atmospheric
pressure is 12 lbs. ?
6. When a certain steam boiler is working at a pressure of
120 lbs. per square inch it is capable of discharging 20 lbs. of steam
per minute. If the pressure be worked up to 150 lbs. per square
inch and maintained there what would be the possible discharge rate ?
7. A cylindrical steel cylinder is 5 feet long and 8 inches in-
ternal diameter and is filled with "Poison gas" at a pressure of
100 lbs. per square inch. What space would this gas occupy when
let out into the air when the barometer reads 30 inches of mercury ?
CHAPTER IV
FORCE, WORK AND ENERGY
Work. We buy coal, not for its own sake, but for
the heal which we can get out of it. We buy gas from
the gas company for the light which we can get from it
in burning. Neither heat nor light can be regarded as
matter : they have no weight and no other property
which we associate with matter.
We classify them as forms of energy and we define
energy as the capabiUty of doing work.
For scientific purposes we have a definite meaning
for the word work, and it is restricted to the production
of motion of matter. We say that when a force acting
upon a body produces motion then work has been done.
Unless motion is produced however no work is done.
Force. In order to produce motion we must apply
force. We have seen already that weight is a force ; we
possess a system for measuring weights and we can
therefore measure our forces in terms of pounds weight,
or grammes weight or any other units of weight that we
care to use. We can also indicate these forces by means
of spring balances so that we can be quite independent
of the force of gravity.
If we raise a bucket of water vertically upwards we
shall have to apply a force which, it can be seen, will
be equal to the total weight of the bucket and its
contents. If we just haul it along the ground without
CH. iv] Force, Work and Energy 49
lifting it the force which we shall have to apply will
depend entirely upon the surface of that ground. If
this is very smooth — like ice — very little force will be
needed to haul the bucket along ; but if the surface be
rough and gritty then the force required might be
considerable.
We can take a better illustration from railway
traction. If we have to raise a truck bodily off the
rails then we must apply a force equal to the total
weight : but if we have to move it along the rails then
it is only necessary to apply a force sufficient to over-
come the friction of the bearings and the rails, and that
force is about 10 to 15 lbs. for every ton which the
truck and its contents weigh. Thus if the truck and
its contents weighed 10 tons then the force to lift it
vertically upwards would be 10 tons or 22,400 lbs. :
but the force necessary to move it along the rails would
only be 100 — 150 lbs. according to the quality of the
truck and the track.
Now work is measured by the force required to
produce the motion and by the amount of movement
produced ; that is to say by the product of the force
producing the motion and the distance through which
the object moves in the direction in which the force is
being applied.
Units of Force and Work. Clearly a unit of work
will be done when a unit of force produces motion
through a unit of length in its own direction. It
follows therefore that we may have many different
units. On the British system the unit most commonly
used is the Foot-Pound — namely the work done when
a force of one pound produces motion to the extent of
one foot in its own direction.
p. Y. 4
'){) Force, Woric and Energy [ch.
In scientific work the units of force chiefly used differ
from the *' weights" which have been given. A unit of
force is defined as tliat force which acting for a unit of
time upon a unit of mass produces a unit change of
velocity. For example it is found that if a force of
7|.V.j lbs. weight be apphed to a mass of 1 lb. mass which
is free to move without friction, it will move and its
velocity will increase by 1 foot per second every second.
Therefore the unit of force according to this definition
is ~~,, lbs. weight. This is called a Poundal.
Similarly it is found that a force of tj^t gramme
weight will cause the velocity of a mass of 1 gramme
to increase by 1 centimetre per second every second.
Thus the metric unit of force is y^y gramme weight.
This is called a Dyne.
Returning to our units of work again we see that
the true unit of work on the British system would be a
foot-pounial, which is ^^ of the foot-pound ; and on
the metric system we have the centimetre-dyne which
is called an erg. This is a very small quantity of
work, and the practical unit of work on the c.G.s.
system is a multiple of the erg, namely 10,000,000 ergs,
and this unit is called a Joule.
1 joule is equivalent to 0-737 foot-pound. This is
the electrical engineer's unit of work.
Mechanical engineers generally prefer to use one
pound weight as a unit of force and one foot-pound as
the unit of work. This means that the engineer's unit
of mass must be correspondingly increased in order to
meet the conceptionjaf a unit of force being that force
which would produce a change of velocity of 1 foot
per sec. in one second when acting on a U7iit mass.
A force of 1 lb. weight would produce a change of 32-2
iv] Force, Woric and Energy 51
feet per sec. in one second on a mass of 1 lb. mass :
but if the mass were increased to 32-2 lbs. mass the
change of velocity per second produced by a force of
1 lb. weight would only be 1 foot per sec. Therefore
the engineer's unit of force is the pound weight and the
unit of mass is 32-2 lbs. No name has been given to
this although the remarkable word slug was once
suggested.
This Ust of units is very dull and uninteresting but
of very great importance. A student who slurs these
over is storing up trouble for himself, for there can
be no doubt that the man who understands all his
units will have little or no trouble with the various
numerical problems of his subjects.
Examples of work. We may briefly illustrate the
use of these units. If a railway truck requires a force
of 100 lbs. to pull it along so that it is just moving
against the friction then the work required will be
100 foot-lbs. for every foot along which it is moved.
Let us find out how many ergs and joules this is equiva-
lent to. Since there are 453-6 grammes to the pound,
the force = 453-6 x 100 grammes weight; and since
there are 981 dynes of force to the gramme weight the
force in dynes = 453-6 x 100 x 981.
Further since there are 30-48 centimetres to the foot
the work done in centimetre -dynes, i.e. in ergs, will be
453-6 X 100 X 981 x 30-48 or 1,356,303,916 ergs. And
since there are 10' ergs to 1 joule the work done in
joules will be 13 5* 63 joules.
If work is done by a force which varies in magnitude,
then the product of the average force and the distance
through which it is applied will give the measure of that
work. The measurement of the work done on the
4—2
52 ■ Force^ Work and Energy [ch.
piston of a steam engine during its motion along the
cylinder is an example of this kind, jand the indicator
diagram represents how the force is changing for each
position of the piston. From the diagram the average
force can be determined (see Chapter XIII).
Energy. We say that a body has energy when it
is capable of doing work and therefore we measure its
energy by the number of units of work it can do.
For example, the weight of an eight-day clock when
wound up to the top is capable of doing a certain amount
of work in falling gradually to its lowest position. If
the weight weighs 7 lbs. and the distance between its
highest and lowest position is 4 feet then when wound
it possesses 28 foot-lbs, of energy which it can give out
to keep the clock going. When it has fallen half-way
it only possesses 14 foot-lbs. of clock energy — the other
14 having been given up.
There are two general divisions of energy. Some
bodies, hke the clock weight, possess energy on account
of their position or state. A compressed spring, a
coiled-up watch spring, a sprung bow, an elevated pile-
driver, a stone on the edge of a cliff and some water
in a high reservoir are examples of things possessing
energy because of their condition, position or state.
We say that these things have potential energy.
Other bodies are capable of doing work because of
their motion. A flying bullet, a falling stone, the water
of a waterfall, the steam forced from a high pressure
boiler, the wind, a hammer head just at the moment
of impact, are examples of things possessing energy due
to their motion. We say that these have kinetic energy.
The energy of a body is capable of being changed
from potential to kinetic and vice versa. Fig. 19 (a)
IV]
Force, Work and Energy
53
represents a pile driver: position A shews the driver
at rest at its highest position where its energy is all
potential : position B represents it moving downwards
towards the pile, and though its potential energy must
be less than it was at A yet it now has kinetic energy
due to its motion : position G represents it at the
moment of impact, and here its potential energy in
relation to the pile is zero but its kinetic energy is
greater than it was at B since it has gained speed.
h
II
1 1
I I
I I
I i
I I
I I
I I
I I
I I
I
E F
(a) (b)
Fig. 19
Fig. 19 (6) represents a pendulum swinging between
extreme positions of D and G. At the positions
D and G it is at rest at its highest position and its
energy is all potential. At F it is at its lowest position
and its pendulum energy is all kinetic. At E its energy
is partly potential and partly kinetic.
The reader will learn that in all these cases the sum
of the potential and kinetic energies at any moment is
a constant quantity; and that what a body loses in
potential energy it gains in kinetic energy.
.')4 rurct, WinL nuil Entiijij [cm.
Principle of the Conservation of Energy. Many ex-
periineiits liave heoii pcrlorinod in comparatively recent
times which go to shew that though we can alter the
jorm of the energy of a body yet we cannot destroy
energy nor yet can we create it. We shall deal with
some of these experiments at a later stage, but it should
be made clear to the reader now that this is regarded as
an estabHshed fact and that it is practically the funda-
mental basis of modern science. It is known as the
principle of the conservation of energy and it is exactly
parallel to the principle that matter can neither be
created nor destroyed though it can be changed in
form and condition.
The reader will ask what happens to the energy of the
pile driver when the driver has come to rest on the pile
head ? It is found that it has been changed into another
form — a form which we call Hmi. With the aid of heat
mechanical work can be done and it has been shewn
that the amount of mechanical work which a given
"quantity of heat" can do is such that if this same
amount of mechanical work be converted into heat it
will produce in turn the same "quantity of heat" as
that with which we started. And further, in whatever
way we do work which produces heat — whether by
friction or by hammering or by boring or by percussion —
we always get the same " quantity of heat" if we do the
same amount of work. This is discussed in detail in
Chapter XIII.
In the same way^heat energy Qan be converted to
light energy. Heat energy can also be converted to
electrical energy, mechanical energy can be converted to
electrical energy which in turn can be converted to
heat or to light or to mechanical energy again. In fact
Tv] Force, Woi'h and Energy 55
it. is just that "flexibility" of electrical energy which
makes it of such use to mankind, for it is so easy to
transmit from one place to another and it is so easily
changed to whatever form or forms we desire. Then
in coal we have a store of chemical energy which changes
to heat in burning ; the heat is given to water and pro-
duces steam at a high pressure charged as it were with
potential energy ; the steam is liberated and its kinetic
energy is given up to the piston of an engine ; the kinetic
energy of the engine is transmitted to the dynamo and
converted to electrical energy ; the electrical energy is
transmitted to where it is needed and there transformed
to any form we wish — to heat, to light, to chemical
energy in secondary cells and in chemical manufacturing
process and to mechanical energy in motors. But all
this energy has come from the boiler furnace ; we have
not made any ; we have not destroyed any ; but we
may possibly have wasted a considerable quantity. We
have not used all the heat given by the coal — much has
gone up the chimney so to speak ; we have produced
heat at all our bearings because we cannot make them
mechanically perfect and frictionless,'and so the energy
necessary to overcome that friction has been changed
to heat.
We may sum up then by saying that energy like
matter can neither be created nor destroyed but that
it can be changed from any one form to any other form
of which it is susceptible.
Power. In scientific work this word has a very
restricted meaning and one which differs considerably
from its meaning in common usage. By power we
mean the rate at which work is done. 20 foot-lbs. of
work may be done in a second or in an hour and though
.")G Force, Work and Energy [ch. iv
the actual ^^'ork done \\ ill be the same in each case yet
the rate of working will be very different. The unit of
power would naturally be the rate of working when a
unit of work is done in a unit of time. In practice,
engineers take as a unit of power 550 foot-lbs. of work
per second which is called 1 horse-power. This is
equivalent to 33,000 foot-lbs. per minute. The elec-
trical engineer's unit of power is 1 joule per second which
is called a ivatt. 1000 watts or 1000 joules per second
is called a Hlowatt and this is more generally used in
heavy electrical engineering. 1 horse-power is equiva-
lent to 746 watts.
It might be well to point out here that a 1 horse-
power motor might be constructed to work at high
speed so that it could, for example, haul up a load
of 1 lb. through 550 feet in a second, whilst another
1 horse-power motor could haul up 550 lbs. through
1 foot in a second. Thus a mere knowledge of the
horse-power does not give ua any idea of the hauling
capacity of the motor or engine and it is entirely wrong
to imagine that a 1 horse -power motor can necessarily
pull with the same puU us that which can be exerted by
an average horse.
The reader can ask himself what is the object of the
gear box of a motor car.
EXAMPLES
1. How much work would be done in pumping 120,000 gallons
of water from a depth of 22 feet ? If this work were done in 2 hours
what would be the rate of working (a) in foot-lbs. per minute, (b) in
horse- power? ^
2. How many ergs of work are equivalent to 1 foot-lb. ? (There
are 45.3-6 grammes per lb. and 2-54 cms. to the inch.)
How many joules of work is this equivalent to and if the work
was done in l/5th sec. what would be the rate of working in watts?
CHAPTER V
HEAT AND TEMPERATURE
It may be well to begin by saying that we do not
know what heat really is. All we can say with any
degree of definiteness is that heat is an agent which
produces certain effects. We can study the nature of
these effects and the conditions under which they may
be produced and their application generally for the
benefit of mankind. A moment's reflection will shew
that we need not necessarily know the precise nature
of this thing which we call heat, although, on the other
hand, we can see that such knowledge might help us
considerably both in the production and use of this
most valuable agent.
We know that heat can produce certain effects.
Our first knowledge is of its comforting effects upon
our person and of its chemical effects upon our food.
And as our vision grows more extended we become
conscious of its effects upon life in both the animal and
vegetable worlds. Then we find how it can change the
physical state of matter from solid to liquid and from
liquid to gas. Then again we begin to realise that it
is an agent which can do work for us. We think of the
steam engine and reflect that after all it is the burning
of the fuel which yields us all the energy ; and further
knowledge shews us that in the gas engine, the oil
i)H Hent nmf Temjterdtnrv [CH.
engine and the petrol engine, combustion and the pro-
duction of heat give us the source of all their energy of
motion. How important then it is that we should
know as much as possible about the various effects
which heat can produce and the various methods of
producing and using it.
Production of Heat. We have already seen that
energy can shew itself in many different forms, and
that one of these forms is heat. We have reahsed that
energy like matter can be changed from one form to
another, and that it can neither be created not yet
destroyed. It follows therefore that whenever we
produce heat it is at the expense of an equivalent
amount of energy which was previously existing in
some other form.
The chief method of production is by the expendi-
ture of chemical energy. All forms of burning or com-
bustion are examples of this, from the combustion of
that great mass which we call the sun down to the
burning of the humble match. If we bum a given
mass of anything — coal or candle — and keep all the
residue we shall find the mass of matter the 'same as
before, but that mass has no longer the energy which
it had before combustion. The heat was obtained not
at the expense of any of the matter or stuff but at the
expense of its chemical energy — that mysterious weight-
less attribute of the coals or candles for which we
really pay when we buy them. We do not really
want the coal as such when we buy it: we want the
chemical energy which it contains and which we can
change to heat energy whenever we desire to do so.
The same statement applies to any other kind of fuel
and to all those fearsome mixtures termed explosives.
v] Heat and Temperature 59
Further it is probably known to most readers that
heat can be produced by chemical changes without
combustion. If some water be added to strong
sulphuric acid heat will be produced at once, and con-
sequently great care must be taken in the dilution of
acids. Further everyone knows how heat is developed
in a haystack if the hay be stacked before it is dry.
The mechanical energy of motion may be changed
into heat. Whenever there is any kind of resistance
to motion — that is to say any kind of friction — heat
is developed in direct proportion to the amount of
energy necessary to overcome that friction. Such heat
is, as a general rule, waste energy ; but as friction is
always present the loss is unavoidable. An engine
driver tests the bearings of his engine by feeling them.
Bad bearings become unduly heated, and the increase
in warmth serves as a danger signal. The striking of
a match is an example of the useful conversion of
mechanical to heat energy. The old flint and tinder,
and the yet older rubbing of dry sticks together are
similar examples. "Shooting stars" are examples of
the heat produced by the resistance of the air to bodies
falling through it at an enormous speed. The melting
of a rifle bullet on striking a steel target affords another
example of the changing of mechanical energy to heat.
Electrical energy can also be converted to the form
of heat and every reader knows something about electric
lighting and heating.
In short whenever work is done without producing
its equivalent in some other form of energy the balance
is shewn in the form of heat..
Temperature. We know that a reservoir of water
is capable of doing work and that such work can only
60 Heat and Temperature [ch.
be done by the motion of some of the water. It can
do work, for example, by a downflow to a water-turbine
and we know that the amoimt of work which the
reservoir can do depends upon the quantity of water
it contains and the height of the reservoir above the
ivater -turbine. That is to say the energy of the reservoir
is measured by the product of the mass of water arid
the height above the turbine, and we coukl get the
same energy out of a reservoir at half the height if it
held twice as much water.
Let us imagine that any furnace or source of heat
is a sort of reservoir of heat energy — the energy de-
pending upon some quantity we will call heat and upon
some kind of height which we will call temperature or
heat-level.
The analogy between this reservoir and the water
reservoir will hold good for most things but it ought to
be borne in mind that it is only an analogy and that we
are taking a considerable licence in comparing heat to
water. But just as we say that water will always flow
from a reservoir at a higher level to one at a lower level
quite irrespective of the size or shape or quantity of
water or amount of energy in those reservoirs, so also
may we say that heat is only transmitted from a body
at a higher temperature to one at a lower temperature
whatever may be the other differences between those
bodies.
We may thus take it that temperature is a sort of
level of heat as different from the agent heat itself as
height or level is different from water. Nobody would
confuse a reservoir of water with its height, yet most
people confuse heat and temperature.
Measurement of Temperature. It will be necessary
v] Heat and Temperature 61
to measure temperatures or differences in temperature
if we are going to make any really valuable investi-
gations into the effects of heat upon bodies. Our
senses enable -us to form a rough estimate of tempera-
ture such as saying that this body is hotter (i.e. at a
higher temperature and not necessarily containing more
heat energy) than that. But our senses are not reliable,
for they can lead us into the declaration that one thing
is hotter than another when they are actually at the
same temperature. An example of this may be fur-
nished at any moment, for if we go into any room which
has been without a fire for some time, having therefore
a uniform temperature or heat level all over, and touch
various articles such as the fender or curb, the hearth-
rug and a table leg, we shall find that they all appear to
have different temperatures. The explanation of this
lies simply in the fact that the articles conduct heat
to or from the body at different rates and so produce
different sensations.
Temperature is measured by means of a thermometer
which depends for its action upon the fact that when
heat is given to matter it generally produces an increase
in volume.
Let a glass flask be taken and filled with water (or any
other liquid) and provided with a cork and tube so that
the water rises to some height A in the tube, as shewn
in Fig. 20. If now some hot water be poured over the
flask it will be noticed that at first the water drops to
a position such as B but soon rises again to such levels
as C and D. We might perhaps imagine that water there-
fore contracts for a moment when heated : but if we heat
the water from within — by means of a small coil of wire
through which a current of electricity can be passed —
()2
Heat and Temperature
CH.
we shall find that there is no initial dnj]). 11 we bend
a piece of glass tube or rod into the fonn of a triangle
and bring the two sides together at the apex so that
they can just grip a coin — as shewn in Fig. 21 — and
then heat the base we shall find that glass expands when
heated ; this will be shewn by the coin dropping from
the apex of the triangle. We therefore conclude that the
dropping of the water in the first instance — when the
hot water was poured over the fiask — ^was due to the
Fig. 21
Fig. 20
glass receiving the heat first and expanding, thus having
a larger volume. But when the heat got through to
the water inside then that expanded too, and since it
ultimately went above its original mark A we conclude
v] Heat and Temperature 63
that water expands more than glass does. As a matter
of fact liquids in general expand more than solids.
Now if we put this flask into vessels of water at
different temperatures we shall find that the water in
the tube will set at a different level for each tempera-
ture.
This furnishes us with the basis of temperature
measurement. We could mark a scale off in any way
we desired and it would be sufficient perhaps for our
purpose — ^but if everybody had his own scale of tempera-
ture we could hardly make any progress. What the
scale is really does not matter ; but it is of first import-
ance that we should all use the same. The well-known
case of the bricklayer's labourer who was sent to make
a certain measurement and came back with the result
as three bricks and half a brick and a hand and two
fingers, furnishes an example. His measurement could
be reproduced by himself — but it was useless to others.
The length of a foot is quite a detail : it is only
important that we should agree to call a particular
length one foot. And the same appHes to temperature
measurement; it is unimportant what a degree of
temperature is, but we must all understand it and agree
to it and be able to reproduce it.
The Fixed Points of Temperature. In making a
scale of temperature it will be necessary to have two
fixed points of temperature to which reference can be
made at any time. One of these — the lower fixed
point — is the temperature at which pure ice melts or
pure water freezes. This is found to be a constant
temperature. The other fixed point — the upper fixed
point — is the temperature of steam over water which
is boiling at standard atmospheric pressure. This is
64 HeM and Temperature [CH.
a rather complicated fixed point, and the reasons for
its complexity lie in the following facts. Firstly the
temperature at which water boils is largely affected by
the presence of any impurities — such as dirt or salt —
whilst the temperature of the steam above the water is
not affected in any way by these. If we throw a few
pinches of salt into a saucepan of boiling water we shall
find that the temperature of the water will rise, but
the temperature of the steam will remain as it was.
Secondly the temperature at which water boils is
slightly affected by the kind of vessel it is boiled in.
Water boils at a slightly higher temperature in glass
than in copper, but the steam temperature is the same
in both. These two points account for the choice of
steam.
Thirdlj^ the temperature of steam depends upon
the pressure to which it is subjected — rising with an
increase of pressure and falling with a decrease. Daily
changes of atmospheric pressure will affect the tem-
perature of steam ; therefore in defining a fixed point
of temperature we must clearly specify that the steam
shall be under some definite pressure. Standard
atmospheric pressure is defined as the pressure equiva-
lent to 30 inches of mercury at sea level in latitude 45°
at the temperature of the lower fixed point.
These fixed points are called the freezing 'point and
the boiling point respectively.
Construction of Thermometer. The usual ther-
mometer consists of a glass bulb and stem containing
mercury or quicksilver. The flask shewn in Fig. 20 is not
quite suitable for temperature measurements. It is too
big : it will absorb a large quantity of heat itself : and
it will need quite a long time to take up the temperature
V]
Heat and Tem2)erature
65
required. But the idea is sound enough and so we make
a small bulb at the end of a tube of thick wall and
very fine bore. That is to say we reduce the whole
thing in proportion so that we get a reasonably small
instrument which will- absorb very little heat. Then
we use mercury instead of water because it conducts
heat better ; it requires less heat to raise the tempera-
ture of the same volume a given amount; it remains
liquid over a wider range of temperature ; and it does
not wet the glass, and therefore runs up and down the
tube with greater ease.
Fig. 22
Fior. 23
We need not discuss the details of filling, sealing and
resting of the thermometer. We need hardly say any-
thing about the marking of the fixed points except to
state that the thermometer bulb and stem as far as
possible should be immersed in steam or in melting ice
under the conditions specified in our statements of the
P.Y. 5
66 Heat and Temperature [CH.
fixed points of temperature. There is no doubt that
every reader will be testing the fixed points of a
thermometer in the laboratory and he can there study
the arrangements which will ic^scinble those shewn in
Figs. 22 and 23.
Scales of Temperature. It is rather unfortunate
that there are three scales of temperature in existence
and use. These three are known as the Centigrade, the
Fahrenheit and the Reaumur respectively. Fig. 24
illustrates the essential features of these scales and
their differences. Celsius, who gave us the Centigrade
scale, called the freezing point 0 — written 0° C. — and
the boihng point 100, and he divided up the interval
into 100 equal parts each of which he called 1° C.
Fahrenheit originally took different fixed points :
he took a mixture of ice and salt and he imagined that
that was the lowest temperature which could be ob-
tained and so called it 0° F. Then he took the tempera-
ture of the human body as his upper fixed point and
called it 100° F. The interval he divided up into 100
equal parts so that his scale was a Centigrade scale,
though different from Celsius' scale. On Fahrenheit's
scale the temperature of pure melting ice was found to
be 32° F., and the boiling point 212° F. Thus the
interval between the freezing and boihng points is 180
Fahrenheit degrees.
Reaumur's scale differs from Celsius' in that the
boiling point is called 80° — because 80 is an easier
number to subdivide than 100 !
Conversion from one scale to another. In this
country both the Fahrenheit and Centigrade scales are
used. The scale in common use is the Fahrenheit, the
Centigrade being used for scientific work and by
V]
H^at mid Temperature
Q7
electrical engineers. Mechanical engineers have gener-
ally used the Fahrenheit but there are signs of the more
general adoption of the Centigrade scale. Conversion
from one scale to another is a simple matter and should
not be beyond the powers of our readers without any
further assistance in these pages.
Upper Fixed Point
Lower Fixed Point
Fig. 24
It need only be pointed out that since 100 Centigrade
degrees cover the same temperature interval as 180
Fahrenheit degrees and 80 Reaumur degrees therefore
1 Centigrade degree = ^ Fahrenheit degree = | Reaumur
degree.
It must also be noted that since the scales start from
different points the Fahrenheit temperature has a sort
of handicap allowance of 32 above the other two. This
5—2
68 Heat and Tem))€ratkre [CH.
allowanoe must be added or subtracted according to
the direction of conversion.
Thus 15°C. = 15C. degrees above the freezing
point,
and since 1 C. degree = f F. degree,
.'. 15 C. degrees = 16 x § = 27 F. degrees,
i.e. 27 F. degrees above the freezing point,
.-. 15° C. = 27 + 32 = 59° F.
Similarly 15° C. = 15 x f = 12° Reaumur.
Again let us convert 113° F. to Centigrade and
Reaumur.
113° F. = 113-32 F. degrees above the freezing-
point = 81 F. degrees,
since 1 F. degree = f C. degree.
.•. 81 F. degrees above the f.p. = --g— C. degrees
above f.p. = 45° C.
and 81 F. degrees above the f.p. = ~^ R. degrees
above the f.p. = 36° R.
All readings below 0° on any scale are called minus
quantities.
Other thermometers. The mercury-in -glass ther-
mometer has a wide range of general usefulness but
when temperatures below — 40° C. (which, by the way,
is also — 40° F. as the reader should verify) are to be
measured, some other form must be employed since
mercury freezes at — 40° C. or F. Grenerally alcohol
is used instead of mercury and it can be used down
to — 1 10° C. For lower temperatures than this
gaseous and electrical thermometers are generally
used. These will be discussed later.
v] Heat and Temperature 69
For temperatures above 250° C. or 482° F. mercury
thermometers must also be superseded. The boihng
point of mercury is 350° C, but unless the upper part
of the stem is filled with some inert gas it cannot be
used beyond 250° C.
For higher temperatures recourse is usually made
to a class of instruments called pyrometers. Some of
these depend upon the expansion of solids, but the
majority in use in engineering practice at the present
time are electrical and depend upon the fact that when
a junction of two dissimilar metals is heated a current
of electricity is generated which increases as the temper-
ature of the junction increases. This current operates
a delicate detector — really a voltmeter— the scale of
which is marked off directly in degrees of temperature.
These are very valuable instruments and are of great
service in measuring any high temperatures such as
superheated steam, flue temperatures, boiler-plate
temperatures and so on. Fig. 25 is a diagram illus-
trating the principle of a pyrometer as supplied by
Fig. 25
Messrs R. W. Paul. We cannot well discuss it in
detail since it is possible that many readers have
not progressed sufficiently into the study of the
sister science of electricity to be able to appreciate
70 Heat and Temperature [CH.
it. Those who have will be able to understand it
well enough from what has been said.
Self-registering Thermometers. If it is desired to
know the highest or lowest temperature reached during
any particular interval of time a self-registering ther-
mometer is used. A simple form (Rutherford's) of
maximum thermometer is shewn in Fig. 26 (a), and (6)
illustrates the thermometer for recording the minimum
temperature. The maximum thermometer is just an
I
D
(a)
Yi.i.^^yyyy^^yyyy.-r^':^:^,
(b)
Pig. 26
ordinary mercury thermometer provided with a little
index I which can slide freely along the tube. As the
mercury expands it pushes the index along and when
it contracts the index will be left /'. The position of
the left-hand end of the index will be the maximum
temperature recorded since the index was last set in
position against the thread of mercury.
The minimum thermometer contains alcohol instead
of mercury and the index is placed inside the alcohol in
the tube. As the alcohol contracts this index will be
drawn back, but when the temperature rises again it
will remain at its lowest point. Of course the index
must be small enough not to impede the flow of alcohol
up the stem. The indexes are set in position by tilting
the thermometer and tapping them gently. In some
forms they are made of iron and are set in position by
means of a small magnet.
v] Heat and Temperahn'e 71
Fig. 27 illustrates the doctor's or clinical thermo-
meter. The bore of the tube is constricted at the
point a. When the mercury is expanding the force
of expansion is great enough to push the mercury
through this narrow part of the tube ; but on con-
tracting the thread of mercury breaks at the con-
i""i'"'r"'i-F'i|""i"ii|""i""i""i""M"'i""i
r)
Fig. 27
striction thus leaving the thread in the stem at the
same position it occupied when in the patient's mouth.
Before the thermometer can be used again the thread
must be shaken down — an operation frequently re-
sulting in disaster to the thermometer.
EXAMPLES
1 . Convert the following Centigrade temperatures to Fahrenheit :
36°, 2000°, - 273°, - 40°.
2. Convert the following Fahrenheit temperatures to Centigrade :
10°, 0°, - 40°, - 400°, 98-4°, 2000°.
3. Convert the followmg Reaumur temperatures to Fahrenheit
and to Centigrade: 12°, - 32°, - 218-4°, 160°.
CHAPTER VI
EXPANSION OF SOLIDS
One of the chief effects of heat upon matter is the
change of volume which it produces. In the vast
majority of cases an increase in the temperature of
a body is accompanied by an increase in the volume,
but there are cases in which the converse is true.
In the case of sohds we may have expansion of
length, breadth and thickness — and this is generally
the case. India-j-ubber in a state of tension contracts
in length when heated — but its volume increases. All
metals however expand proportionately in all direc-
tions. If a sphere of metal be heated it will expand
but will still be a sphere. All metals expand with
increase in temperature and contra<)t with decrease in
temperature, and metals expand more than any other
solids under the same conditions. Further, different
metals expand differently under equal conditions.
Laws of expansion. We will consider firstly the
expansion of length or Hnear expansion of a substance.
It has been shewn — and can be shewn again by the
apparatus illustrated in Fig. 28 — that the length of a
solid increases uniformly with the increase in tempera-
ture. An increase of 20° of temperature will produce
twenty times the increase in length which would be
produced by a 1° increase in temperature.
CH. vi] Expansion of Solids 73
Secondly it can be shewn in the same way that the
actual amount of expansion produced for a given in-
crease in temperature depends upon the original length
of the substance. That is to say a 10 foot length of
metal would have a total expansion 10 times greater
than a 1 foot length of the same metal for the same
increase in temperature.
Thirdly, the expansion produced depends upon the
substance which is expanding. Obviously if we wish
to compare the expansion of different substances we
must take equal lengths and heat them through equal
ranges of temperature. It is also obvious that it would
be most convenient to take unit lengths and to heat
them through 1° of temperature.
Coefl&cient of linear expansion. The increase in
the length of a unit length produced by increasing the
temperature 1° is called the coefficient of linear expansion
of a substance.
Strictly, the definition given above is not true. It
should be the increase in the length of a unit length at
the freezing point when increased 1°. But the value of
the coefficient is so small that for all practical purposes
the definition with which we started is sufficiently
accurate and is certainly simpler.
A foot of brass when heated 1° C. becomes 1-0000188
foot. Similarly 1 centimetre . of brass when heated
1° C. becomes 1-0000188 centimetre. From our defini-
tion it follows that the coefficient of linear expansion
of brass is 0-0000188 per degree Centigrade, and we can
readily see that if an increase of 1° C. produces an
increase in length of 0-0000188 unit, then an increase
of 1° F., which is only {}th of a degree Centigrade, will
only produce an increase in length of {} x 0-0000188 or
74 Expansion of Solids [ch.
0-00001044 unit. That is to say the coefficient of
expansion per degree Fahrenheit will only be fjths of
that per degree Centigrade.
Again though we have only spoken of exjjansion,
the same laws exactly apply to contraction produced by
a decrease in temperature, and we might even define
the coefficient of expansion (or contraction) as the
increase (or decrease) in the length of a unit length of
a substance for an increase (or decrease) of 1° of tem-
perature.
Calculations. Calculations are obviously quite
simple for we have only to remember that the increase
(or decrease) in length is directly proportional to
(tt) the increase (or decrease) in temperature,
(b) the original length,
(c) the coefficient of linear expansion of the sub-
stance,
and we can apply the simple rules of proportion.
There is clearly no need to deduce any formula for such
straightforward work.
Example. A rod of copper is 33" long at 15° C. :
what will be its length at 100° C, the coefficient of
linear expansion of copper being 0-0000172 per degree C.
It follows therefore that
1 inch of copper heated through 1° C. expands by
0-0000172 of an inch, .
.'. 33 inches of copper heated through 1° C. will
expand by 33 x -0000172",
.*. 33 inches of copper heated through 85° (i.e.
100-15) will expand by 33 x 85 x -0000172"
- 0-048246".
Therefore the length of the rod at 100° C. will be
33-048246" or, as we should express it in practice, 33-048".
VI]
Expansion of Solids
75
Determination of coefficient of linear expansion.
Fig. 28 illustrates a simple form of apparatus which
can be used to determine the coefficient of expansion
of a solid. The rod R to be tested is placed inside a
jacket J which can be filled with steam or water at
any desired temperature. The rod is fixed between
two screws as shewn, AS being an adjusting screw and
MS a micrometer screw. The micrometer is adjusted
to zero and the rod is tightened up by means of the
adjusting screw. This should be done at the higher
temperature first. Then the temperature of J is
lowered and the micrometer screw is turned until the
Fig. 28
rod is tight again. The decrease in the length of the
rod is thus given by the micrometer screw : the original
and final temperatures are given by the thermometer :
and the original length of the bar is obtained by re-
moving the rod and measuring it with a straight-edge.
From these particulars the coefficient of linear expan-
sion may be calculated.
The above method is not very accurate, the chief
source of error lying in the expansion and contraction
of the screws. But it will serve to illustrate the general
principle and the reader will be quite able to understand
7(5
Eaypaiision of Solids
[CH.
the many more refined arrangements for this measure-
ment if he understands this one.
Table shewing some coefficients of linear expansion
per (legrec Ceriliijrade.
Zinc
Copper ...
Iron, sof t . . .
Steel, soft
Nickel steel (^li^o nickel
Nickel steel (45 % nickt
Cast iron
Tin
Lead
Silver
Gold
Platinum .
Porcelain .
Glass (soft)
These numbers represent
... 000(X)294
0-()000172
0(XX)0122
0-0(XX)108
) ... 0-00000087
1) ... 0-0tKX)082
... 0-0(X)011
... 0-000025
... 0-000028
... 0-000021
... 0-000015
... 0-000009
... 0-0000088
... 0-000009
average values only.
Some advantages of expansion and contraction. Much
practical advantage can be taken of the expansion and
contraction of substances due to temperature changes.
The forces exerted by the expansion or contraction may
be very great and they are used to advantage in such
operations as fixing iron tyres on wheels and other
"shrinking" operations. The tyre is made of such a
size that it will just fit on to the wheel when it is hot
and the wheel is cold. When the tyre cools it grips the
wheel tightly. Similarly one sleeve or cylinder may
be shrunk on to a smaller cylinder.
Then we have a very universal application in the
case of hot ri vetting. The plates are drawn tightly
together by the rivetters with their hammers— but the
vi] Expansion of Solids 77
contraction of the rivet as it cools will always exert an
additional force.
The forces exerted by expansion and contraction of
an iron bar may be shewn very strikingly by means of
the apparatus sketched in plan in Fig. 29. JS is an iron
bar having a screw thread and a large nut S at one end
and a hole through which a cast iron pin P is inserted
at the other end. The screw can be adjusted so that
the bar is held rigidly between the end fixtures on the
metal base. If the bar is heated the pin P will be broken
or the bar B will buckle. The force of contraction can
also be shewn by placing the pin and the nut on the
other sides of the end fixtures and tightening up whilst
the bar is hot. On cooling the pin will be broken.
Fig, 29
Small automatic switches for switching an electric
lamp on and off at frequent intervals are amongst other
applications of the expansion of metals.
If two equal lengths of different metals be rivetted
together closely then when this compound bar is heated
it will bend so that the metal which expands the greater
amount will be on the outside of the curve. On cooHng
it will bend in the opposite direction. Fire alarms
which operate an electric bell are often made on this
principle, and the balance wheel of a watch is compen-
sated in the same way.
78 Ea^pcmmcm of Sollth [ch.
Some disadvantages of expansion and contraction.
Nobody suffers more from the drawbacks of expansion
than the engineer. Fortunately the effects can always
be compensated — but such compensation has to be
nicely adjusted and necessarily adds to the cost. Every-
one knows why railway lines are laid in sections, why
no two rails butt on to one another, why the rails are
"fixed" in chairs with wooden wedges, and why they
are "fixed" together with fish plates. And a" httle
calculation will shew why the lengths of the rail sections
in use are not greater than they are. It would be bad
for rolling stock, rails and passengers if we had to
leave large gaps between sections : and even as it is
there is a distinct difference between summer and winter
travelling.
Tramway rails are buried— and thus we have not
the same trouble because the rail temperature will
never differ appreciably from the earth temperature.
But of course it is too costly a method for long distance
railways.
Every branch of structural engineering has to take
this expansion and contraction into consideration.
The Forth Bridge is built in such a way that a total
change of length of 18 inches must be allowed for
between winter and summer. Clearly, it must not
be taken up all at one place.
Furnace bars must fit loosely : pipe joints of exposed
gas or water mains must be telescopic : patterns for
castings must be Qf such a size that they take account
of the contraction of the metal, and sometimes must be
designed specially to prevent fractures which may be
produced by one part of the casting coohng quicker than
another part and setting up undesirable stresses.
VI]
Expansion of Solids
79
I
The standard yard measure is only correct kt one
temperature, 60° F.
A clock regulated by a pendulum will gain or lose
as its pendulum contracts or expands. There are many
devices for compensating pendulums all
of which depend upon the fact that
different substances expand differently.
The gridiron pendulum affords us a
useful example since this principle is
also applied to other compensations.
Fig. 30 illustrates this. Two different
metals are used, iron and zinc. The
iron rods can expand downwards and
the zinc rods can expand upwards.
The lengths of / and Z are chosen so
that the total expansion of the iron
is the same as that of the zinc. In
this way the position of the centre of
gravity of the pendulum bob will re-
main constant.
Surface or superficial expansion.
If we take a square of a metal of side
1 foot and heat it, it will expand in all
directions. If we heat it 1° and if its
coefficient of expansion is K then each
side will he, {\ + K) feet. Therefore its
area wiU become (1 + KY square feet, Fig. 30
that is 1 + 2K + K^ square feet. That is to say the
coefficient of superficial expansion is {2K + K'^). Now
since K is always a very small quantity it follows that
K^ will be much smaller and indeed is so small that
it can be neglected in comparison with 2K. It is
therefore usual to say that the coefficient of superficial
}{0 E.vpansicni of Sol'uh [CH. vi
expansion is twice that of linear expai}f<ion and of course
is expressed in square meoMire.
Cubical or voluminal expansion. In the same way
if we take a cube of 1 foot side and heat it 1° of tempera-
ture each side will become I + K feet and its volume
will become {I + Kf cubic feet or I + 3K + 3K^ + K^
cubic feet. The coefficient of cubical expansion is thus
{3K + 3Z2 + K^) but again we may neglect {3K^ + K^)
in comparison with 3K, and it is usual to say that the
coefficient of cubical expansion is three times that of
linear expansion expressed in cubic measure.
EXAMPLES
1. What is the expansion of an iron rail 37 feet long at 00° F.
when it is heated to 140° F. ? The coefficient of expansion of the
rail = 0-000012 per degree Centigrade.
2. The distance from London to Newcastle is 27 1 miles. What
is the total expansion of the rails between the lowest winter tempera-
ture (say 10° F.) and the highest summer temperature (say 120° F.) ?
3. What must be the length of a rod of zinc which will expand
the same amount as 39-2 inches of iron? See table on p. 76 for
coefficients of expansion.
4. A plate of copper is 10" x 8" at 15° C. What will be its
area at 250° C. ?
5. A sphere of brass has a diameter of 2-2"' at 32° F. What will
be its volume and what its diameter at 212° F. ?
6. The height of a barometer at 15° C. is found to be tO cms.
when measured with a brass scale which is correct at 0° C. What
is the true height of the barometer ?
7. A certain rod is 36 inches long ai 0° C. and 30-04 inches at
50° C. What is the coefficient of expansion of the rod ?
CHAPTER VII
EXPANSION OF LIQUIDS
Obviously we are only concerned with change of
volume in the case of liquids, since they have no
rigidity. Further they must be in some kind of a
containing vessel and since in all probability this will
expand we shall have to be careful to distinguish
between the real and the apparent expansion of the
liquid. The experiment illustrated by Fig. 20 indicates
this. If we know the increase in the volume of the
containing vessel and the apparent increase in the
volume of the liquid the real expansion of the liquid
will be the sum of the two.
The coefficient of real expansion will therefore be
greater than the coefficient of apparent expansion by
an amount equal to the coefficient of expansion of the
material of the containing vessel.
Most liquids— molten metals excepted — do not ex-
pand uniformly. Fig. 31 is a graph illustrating the
relationship between the volume and the temperature
of a given mass of water. It is seen that the change
in volume per degree of temperature is an increasing
quantity after a temperature of 4° C. has been passed.
It is therefore clear that we cannot give a number which
represents the coefficient of expansion of water. We
can give it for a definite range of temperature, but that
P.Y. 6
82
ExpansiitH <>/ Liquids
[CH.
is all. Thus between the temperatures of 4° C. and
14° C. the mean coefficient of expansion (real) of water
is 0-00007. but between the temperatures of 50° C. and
60° C. it is 0-00049.
1-0020
1-0010
1-000
/
^^
^
/
(
fC 4° {
>" 1
0° 1
5° 20°
Temperature
Fig. 81. Volume and Temperature of Water
Methods of determination of coefficient of expansion.
The apparent coefficient, in glass, may be obtained
readily by means of a glass bulb (of known volume)
having a stem graduated in terms of the bulb's volume.
This is filled to a certain point up the stem. It can
then be immersed in a bath the temperature of which
can be adjusted to any desired value, and the apparent
volume at each temperature can be read off.
The real or absolute expansion is usually determined
by comparing the density of the liquid at one known
temperature with its density at 0° C. or at any other
known temperature. As density is the mass of a unit
volume it follows that as the volume of a given mass
I
VIl]
Expansion of Liquids
83
increases, its density decreases. Fig. 32 illustrates a
form of apparatus by means of which this measurement
may be made. The hquid to be tested is placed in the
large U-tube, each limb of which is surrounded by a
/
Steam inlet
Steam
outlet
-^
-^~
& Water
I outlet
Cold water
Fig. 32
jacket through which we can run cold water or steam
or water at any desired temperature. The U-tube is
open to the atmosphere and if both limbs are at the
same temperature the liquid will be at the same level
in each. If we pass ice cold water through one jacket
6—2
84 E.rjMUision of LiqultLs [oh.
and steam through the other then the density of Hcjuid
in the hot hmb will be less than that in the cold limb
and therefore we shall get a difference in level since
a longer column of hot liquid will be needed to balance
a given column of cold liquid. We then measure the
heights of the columns H and h and note the tempera-
ture of the two jackets.
The heights H and h are inversely proportional to
the densities which we may call Dq and D^ .
The densities are inversely proportional to the
volumes.
Therefore the heights are directly proportional to
the volumes.
That is to say H : h = volume at the higher tem-
perature : volume at the lower temperature.
Therefore the coefficient of expansion between the
temperatures chosen
, H-h
A (difference in temperature) '
There have been several elaborations of this prin-
ciple of measurement notably by Regnault and Callendar :
but the fundamental principle is the same and the
elaborations aim at producing greater accuracy.
Peculiar behaviour of water. If we look at Fig. 31
again we notice that as the temperature of water is
increased from 0° C. the volume of the water decreases
and becomes a minimum at 4° C. after which it increases
again. Water is unique in this respect and the tempera-
ture at which th6 water has its least volume is known
as the temperature of maximum density, namely 4° C.
or 39-2° F. The unit of mass on the metric system is
one gramme, which is the mass of a cubic centimetre of
water at 4° C.
%
vii] Expansion of Liquids 85
The immediate effect of this pecuUar behaviour of
water is the preservation of animal and vegetable life
in lakes and ponds in winter time. The water below
the ice will never fall below this temperature of 4° C,
or 39-2° F. because at any other temperature higher or
lower it will be Ughter bulk for bulk and will therefore
remain on top. As a pond cools down (it should be
noted that this cooling will only take place at the
surface) the water at the top will contract and sink
until the whole pond is at 4° C. On further cooling
the surface water will become lighter and will remain on
the top and so will ultimately freeze. But the water
below the ice will be at 4° C. Water and ice are bad
conductors of heat and thus the pond will never become
frozen to any great depth. It is well known that an
ice coating on a pond should be flooded each night if it
is desired to get thick ice on the pond.
The table given below shews how the density and
the volume of water changes between the temperatures
of 0° C. and 8° C.
Temperature
Density
Relative volume
0°C.
0-99987
100013
2°C.
0-99997
1-00003
4°C.
1-00000
1-00000
6°C.
0-99997
1-00003
8°C.
0-99989
1-00012
CHAPTER VIII
EXPANSION OF GASES
As we saw in Chapter III the volume of a gas depends
upon the pressure to which it is subjected. It therefore
follows that in considering how volume changes with
temperature we shall have to be careful to keep the
pressure of the gas constant,
Charles found that gases expand uniformly and that
as far as he could ascertain all gases have the same
coefficient of expansion, namely 0-00366. As a matter
of fact later experimenters have found that this is not
strictly true, but it is sufficiently near the truth for our
purpose.
Gases expand much more than do soHds or Uquids
under equal conditions and we have therefore to be
more careful and particular about our definition of the
coefficient of expansion. We must remember that the
coefficient of expansion of volume of a gas is the increase
in volume of a unit volume at 0° C. when heated from 0°
to 1° C.
We had better look at the importance of this. Let
us suppose for exa6iple that that coefiicient of expansion
was ^th. Now a volume of 1 at 0° C. would become
M at 1° C, and 1-2 at 2° C. and so on. But if we take
the volume of 1-1 at 1° C. and to find its volume at
2° C. we were to take jj^ ol 1-1, viz. 0-11, and add this
CH. viii] Expmisimi of Gases 87
on to the original volume we should get a volume of
1-21 at 2° C.
This does not agree with the result we get by working
from 0° C. So that if we are given that a certain gas
has a volume of 1-1 at 1° C. and we are asked to find
its volume at 2° C. we must first find what its volume
would be at 0° C. and calculate from that point.
In cases where the coefficient is small we need not
bother to find the volume at 0° C. since the error caused
would be quite negligible for practical purposes. We
have adopted this view already in our examples on the
expansion of solids, but in the case of a gas it will be
necessary to work from the temperature of 0° C
Charles' Law. Charles' law states that if a given
mass of a gas be kept at a constant pressure and heated, the
increase in the volume will be directly proportional to the
increase in the temperature.
If we represent the volume of a given mass of gas
at constant pressure by Vq at 0° C. and by Fj at some
temperature t° C. then according to our definition the
coefficient of expansion K will be given by
Fo(«-0) FoX^ '
i.e. the change in volume per unit volume at 0° per
degree C.
/. F,-Fo=FoxZx«,
.-. F, = (Fo X Z X 0 + Fo,
or Vt == Fo (1 + Kt).
Therefore we can easily find the volume at 0° C. and
from that we can find the volume at any other desired
temperature.
Example. A given mass of a certain gas is 12 c.c.
iW Expansion of Gaaes [ch.
at a temperature of 15° C. ; what will it be at 60° C,
the coefficient of expansion being 0-00366 ?
Firstly we find the volume at 0° C.
^15= ^o(l + -00366 X 15),
12 = Fo(l + 15 X -00366),
Then we find the volume at 60° C. from
^60= ^o(l + -00366 X 60),
.-. F6o= 11-375 X 1-2196
= 13-875 c.c.
Experimental verification. Charles' law may be
verified and the coefficient of expansion of a gas
determined by the dilatometer method similar to that
described in the previous chapter.
A bulb of known volume having a graduated stem
can be arranged as shewn in Fig. 33. The bulb and
Fig. 33
part of the stem can contain air or any other gas and
this is shut off from the outside air by means of a small
pellet of mercury P which also serves as an index. If
the volume of the bulb is fairly large compared with
the stem the errors due to the exposed part of the stem
will be very small, but the range of temperature which
can be covered will not be very great. This should be
viii] Expansion, of Gases 89
determined by a preliminary experiment. Then the
bath is heated up to the highest permissible temperature
and readings are taken, as the bath cools, of tempera-
tures and volumes. These can be plotted graphically
and coefficients can be calculated from the various
readings. The volume at 0° C. can be determined by
experiment or can be obtained from the graph.
Any bulb and stem may be readily calibrated by
filling with mercury, and then weighing the mercury
required. Similarly the volume per inch of tube can
be determined by measuring the length of any pellet
of mercury in the tube and then weighing it. From
the density of the mercury and its mass the volume
is calculated since density is the mass of a unit volume.
There are again many more refined and elaborate
devices for the verification of Charles' law, but if the
principle of this is understood, the refinements can be
appreciated quite readily by the intelligent student.
Variation of Pressure with Temperature. We all
know that if we confine a gas to a given space and heat
it the pressure of that gas increases. Such pressure
plays the all-important part in internal combustion
engines and in the use of explosives. We have all
witnessed the disasters to our air balloons in bygone
days when they got too near to the fire.
Regnault shewed that if the volume of a given mass
of a gas was kept constant and its temperature increased
the increase in the pressure was directly proportional
to the increase in temperature.
He found moreover that the coefficient of increase
of pressure — namely the increase in the pressure of a
unit pressure at 0° C. when heated 1° C. — was the same
as the coefficient of increase in volume, -00366 or ^j.^.
90
Exj/ansiou of (jiittfs
L<;ii.
Fig. 34
A simple form of apparatus for the verification of
this law is shewn in Fig. 34. A hulb which contains
the gas O is immersed in a bath B the temperature of
which can be varied at will
and determined by the ther-
mometer T. The bulb is con-
nected by a fine bore tube to
one of the limbs of a U -tube —
similar to the apparatus used
for the verification of Boyle's
law (page 43). By raising or
lowering the right-hand limb
R the mercury in the left-hand
limb can be kept at the same
position for various tempera-
tures of the bath. The actual
pressure of the gas at each
temperature will be the atmospheric pressure in inches
or centimetres of mercury plus or minus the difference
in the levels of the mercury in L and R in inches
or in centimetres — the volume of the gas being kept
constant at each temperature by the adjustment
of JR.
Absolute zero of temperature. If, instead of using
a mercury thermometer for the measurement of tem-
perature, we use a gas thermometer — either on the
constant volume or on the constant pressure principle —
we should find a theoretical minimum temperature
below which we^ could not use it. That is to say if we
assume for a moment that the law of Charles and the
corresponding pressure-temperature law hold good for
all temperatures we should find that at a temperature
of — 273° C. gases would have no volume and would
viii] Expansion of Gases 91
exert no pressure. This temperature is called the
absolute zero of the perfect gas thermometer.
Now it is not considered possible to annihilate
matter at all, so that we must feel that there is a way
out of this mystery. It lies in the fact that gases
change into liquids before they reach that temperature
and after that they no longer follow Charles' law.
According to the Kinetic Theory of Gases (page 8)
the pressure of a gas is caused by the agitation or bom-
bardment of its molecules. Therefore if the gas exerted
no pressure its molecules must be stationary. It is
further suggested that as a body contains more and
more heat the movement of its molecules is increased
and vice versa. Therefore if we can reduce a gas to
such a temperature that it exerts no pressure there
will be no molecular movement and no heat. That
temperature would therefore be the lowest possible or
the absolute zero of temperature.
The temperature of — 273° C. has never been
reached in practice although in recent times the
temperature of — 269° C. has been obtained.
Fig. 35 shews a volume -temperature graph, volumes
being plotted vertically and temperatures horizontally.
If we get readings of the volume of any mass of a gas
between 0° C. and 100° C. and then produce the graph
backwards (assuming Charles' law to hold good) until
the volume is zero we find that the temperature for this
condition is - 273° C.
It will be quite clear to our readers that if this point,
— 273° C, were made the origin of the graph, that is to
say if it were both a zero of temperature and volume, we
could say that the volume was directly proportional to
the temperature calculated from this zero.
92
ExpanMOit of Gaiio
[CH.
From tills we have adopted another temperature
scale — called the Absolute scale — having the tempera-
ture of — 273° C. as its zero and being equal to the
Centigrade scale reading + 273. Thus 0° C. = 273° A.,
57° C. = 57 + 273 = 330° A.,
and - 38° C. = - 38 + 273 = 235° A.,
and so on. Charles' law may now be stated thus:
©"A 73'A
-IOO°C
I
I
I
I73''A
IOO°C 200°C
Temperature \
I I I
273°A 373°A 473°A
Fig. 35
that the volume of a given mass of a gas kept at a constant
pressure varies directly with the absolute temperature.
Thus if PJi be the volume at Tj° Absolute, and Fg
be the volume at ^2° Absolute, then
Fi ^ Tj _ tj° C. + 273
Fa" T2"^2°C. + 273'
In the same way it can be seen that if the volume
viii] Expansion of Gases 93
is kept constant the pressure will vary directly as the
absolute temperature :
P, ^ TIA.
P2 ^2°A.-
Finally if we consider possible variations of each of
the three quantities pressure, volume and absolute tem-
perature, we shall find that
when Pj, Fj and T^ are the pressure, volume and
absolute temperature in one case, and Pg, V2 and T^
those in the second case.
Examples. (1) Let us take the example on page 88.
A given mass of a gas is 12 c.c. at 15° C. ; what will
it be at 60° C. ?
Vi Ti . 12 _ 15+273 _ 288
Fa ~ ^2 ' • • F2 " 60 + 273 ~ 333 '
••• ^2= ^-^jgl^- 13-875 c.c.
We see that it is much easier to solve the problem
this way.
(2) A mass of air has a volume of 24 c.c. at a
temperature of 27° C. and a pressure of 30" of mercury.
What will'be its volume at 77° C. and a pressure of
20" mercury?
•^2^2 ^ 2
24 X 30 300
• • F2 X 20 350 '
„ 24x30x350 ,„
•• ^^ = -20-^3-00 ^1^^-
Absolute-Fahrenheit scale of temperature. Before
94 Expamion of Gases [CH. viii
concluding this chapter it may be well to point out that
the absolute zero of temperature on the Fahrenheit
scale would be — 459- 2°. By adding 459-2 to any
Fahrenheit reading we shall get an Absolute-Fahrenheit
scale. This scale could be used for the above calcula-
tions.
For example : If a certain gas has a volume of
12c.c. at 59° F., what will be its volume at 140° F.?
Fi _ Ti°A.
F2 T2°A.'
and using the Absolute-Fahrenheit scale T^ is
459-2 + 59 = 518-2°
and Tg is 459-2 + 140 = 599-2°,
12 518-2
• • F2 ~ 599-2 '
. „ 12 X 599-2 ,^„^^
EXAIklPLES
1. A certain mass of air has a volume of 50 cubic inches at
16° C, what will be its volume at 0° C. and at IW V.. the pressure
being constant ?
2. A certain mass of air has a volume of 3 cubic feet when the
temperature is 27° C. and the pre-ssure is 15 lbs. per square inch:
what will be its volume when the temperature is 227° C. and the
pressure is 150 lbs. per square inch ?
3. A certain mass of a gas at a temperature of 59-8° F. has a
volume of 36 cubic feet, the pressure being 20 lbs. per square inch.
If the temperature be increased to 212° F. what must be the pressure
in order to keep the volume the same ?
4. The volume of a certain mass of gas is 8 cubic feet at 15 lbs,
pressure and temperature 20° C. If the pressure be doubled find the
temperature to which it must be heated so that its volume becomes
6 cubic feet.
CHAPTER IX
MEASUREMENT OF HEAT
One of the effects which heat may produce when
given to matter is an increase in temperature. This
effect is not inevitable, but generally speaking a body
becomes hotter when it receives heat. An exception
may be quoted at once. If we put a vessel of water
over a furnace we shall find that the water will get
hotter and hotter (as shewn by a thermometer placed
in it) until it starts to boil. But we shall find that it
does not get any hotter after that. We may increase
the temperature of the furnace as much as we please
but the thermometer will not rise beyond the boiling
point. Of course the water will boil away more quickly,
and the heat is being used to produce this change of the
state of the liquid.
However, whenever heat is given to a substance
which is neither at its boiling point nor melting point
an increase in temperature will follow. It is readily
conceivable that if two equal quantities of a substance
are given equal quantities of heat they will be equally
affected so far as temperature increase is concerned.
It is also conceivable that if a certain quantity of heat
be given to a substance and it produces a certain in-
crease in its temperature, twice the quantity of heat
will produce twice the increase in temperature. For
96 Measurement of Heat [ch.
all practical purposes this is true (just as a pint of
liquid will rise to twice as great a level in a cylindrical
vessel as half a pint) but actually it is not strictly the
case. We shall, however, assume that it is, since the
very small error involved is of little or no account in
engineering practice.
Unit of Heat. A unit quantity of heat energy is
defined as that quantity necessary to raise the tempera-
ture of a unit mass of water through one degree of
temperature.
Thus on the British system of measurement a unit
of heat is the heat necessary to raise the temperature
of 1 lb. of water through 1° F. This is called a British
Thermal Unit and is commonly used by mechanical
engineers.
The quantity of heat necessary to raise the tem-
perature of 1 gramme of water through 1° C. is the
unit of heat on the metric system of measurement.
This is called a Calorie.
These units are not equal of course : and since there
are 453-6 grammes to the pound and ^ of a degree
Centigrade to the degree Fahrenheit it follows that
there are 252 calories to the British thermal unit.
It will be noted that water is chosen ^s the standard
substance. We shall see presently that different sub-
stances require different quantities of heat per lb. to
produce one degree rise in temperature.
Every unit mass of water will require a unit of heat
for every degree its temperature is raised : and con-
versely, on cooling, every unit mass will give out a unit
of heat per degree fall in temperature. Thus the heat
necessary to raise the temperature of 3 lbs. of water
from 60° F. to 212° F. will be 3 x (212 - 60), viz.
ix] Measu7'ement of Heat 97
3 X 152 or 456 b.th.u. The heat given out by 4-5 lbs.
of water cooHng from 60° F. to 32° F. will be
4-5 X (60 — 32), viz. 126 b.th.u. That is to say the
heat required or yielded by any mass of water M when
it undergoes a change of temperature from t-^ to t^
will be
M X (^2° - ^1°) units.
The units will be calories if M is in grammes and
t^ and ^2 s-re Centigrade ; and they will be British
thermal units if M is in lbs. and ^^ and t^ are Fahrenheit.
Specific Heat. If we take equal masses of iron and
copper and heat them to the same temperature and
then plunge them into two equal vessels of water at
the same temperature, we shall find that the vessel
into which we plunged the iron will become a little
hotter than the other one. This suggests that the iron
must have given out more heat than the copper. The
heat given out must have been received by the water :
and its temperature would rise. In the same way if we
take equal masses of other different substances at equal
temperatures and plunge them into separate equal
vessels of water we shall find that these different sub-
stances give out different quantities of heat.
The quantity of heat necessary to raise the temperature
of a unit mass of a substance through 1° is called the
specific heat of that substance.
The specific heat of copper, for example, is 0-094.
That is to say 0-094 British thermal unit of heat will
raise the temperature of lib. of copper through 1° ^,
It also means that 0-094 calorie of heat will raise the
temperature of 1 gramme of copper through 1° C
9H
Meamtrement of Meat
CH.
The following table gives the specific heats of some
substances :
«ilvfr (»or)r)
Copper ()()!»4
Iron 0112
Mercury ... . . ... ... OO'.i'.i
Glass ()•!!)
Turpentine ... ... ... ... 0-43
AluminiuTu ... ... ... ... 0-21
Lead 0031
Water • 1
Ice 0-502
Hydrogen (constant pressure) ... 3-402
Air (constant pressure) 0-2427
Air (constant volume) 0-171.5
The fact that water has such a high specific heat
compared with most other things is not generally
appreciated by the man in the street. He is always
inclined to think that a kettle absorbs as much if not
more heat than the water it contains, and may even
advocate the use of thinner kettles. Let us consider
how much heat will be absorbed by a kettle made of
copper, weighing 2 lbs., and containing 3 lbs. of water
when heated from 70° F. to 212° F.
Firstly, the kettle :
1 lb. of copper heated through 1° F. will require
0-094 unit of heat,
therefore 2 lbs. of copper heated through 1° F. will
require 2 x 0-094 units of heat,
therefore 21bs. of copper heated through (212 — 70)°F.
will require 142 x 2 x 0-094 units of heat.
That is to say the kettle will absorb 26-7 units.
ixj Measurement of Heat 99
Secondly, the water :
1 lb. of water heated through 1° F. will require
1 unit of heat,
therefore 3 lbs, of water heated through 1° F. will
require 3 units of heat,
therefore 3 lbs. of water heated through (212 — 70)°F.
will require 3 x 142 units of heat.
That is to say the water will absorb 426 units.
Thus we see that the total heat absorbed by the kettle
and the water is 452-7 units of which only 26-7 units
are taken by the kettle.
Water Equivalent. We could have taken it in a
simpler way than this. Since 1 lb. of copper only
absorbs 0-094 unit of heat for each degree rise in tem-
perature, we can say that 1 lb. of copper is only
equivalent to 0-094 lb. of water, since 0-094 lb. of water
would absorb 0-094 unit for each degree increase.
Therefore we could say that the kettle — viz. 2 lbs, of
copper — was equivalent to 2 x -094, viz. 0-188 lb. of
water, so far as the absorption of heat is concerned.
We could then take it that the kettle and the water
were together equivalent to 3-188 lbs, of water, and if
3-188 lbs, of water are heated from 70° F, to 212° F.
the heat required will be 3-188 x (212 - 70), viz.
452-7 units, which agrees with the previous answer.
Thus we can say that the mass of any substance
multiplied by its specific heat is the water equivalent of
that substance. This is of some assistance to us in our
experiments connected with the measurement of heat.
Measurement of Specific Heat. The substance
whose specific heat is to be determined must be weighed,
and it is heated in some way or other to some known
or measurable temperature. It is then dropped into
7—2
100 Measurement of Heat [ch.
a vessel containing a known quantity of water at
a known temperature. The "mixture" is thoroughly
stirred and its temperature is taken. From these particu-
lars the specific heat of the substance may be calculated.
It will be seen at once that there are certain practical
difficulties connected with this experiment. Pre-
cautions must be taken to avoid loss of heat as the
substance is being dropped into the water ; and again,
precautions niust be taken to prevent loss of heat from
the water to the surrounding air.
The vessel containing this water is usually called a
calorimeter and generally consists of a cyhndrical copper
vessel which is suspended inside a similar but larger
vessel by means of three silk threads. The surfaces
are kept well polished and the calorimeter losses are
thus reduced to a minimum. In addition to this it is
usual in important measurements to arrange that the
first temperature of the water in the calorimeter shall
be as much below the temperature of the surrounding
air as the second temperature is above. In this way
we get a slight gain balancing off a slight loss.
The arrangement for heating the substance generally
takes the form of a steam jacket J, J as shewn in Fig. 36.
The substance S is suspended inside and a thermometer
T is fixed near it. The heater is fixed on an insulating
base with a sliding shutter which has the effect of
opening or shutting the heater. The calorimeter is
placed directly beneath the centre of the heater. When
the jacket is heated and its temperature has been
noted, the shutter is opened and the substance is lowered
into the calorimeter as speedily as possible. The calori-
meter and its contents are then removed, stirred, and
the temperature read.
IX]
Measurement of Heat
101
Let us suppose that the following results were
obtained.
Mass of calorimeter empty 45 grammes.
Material of calorimeter, copper of specific heat 0-094.
(N.B. Only the inside vessel should be weighed as
the outer vessel does not absorb any heat.)
Mass of water in calorimeter 132 grammes.
Original temperature 15° C.
Shutter
Calorimeter
Fig. 36
Mass of substance in calorimeter 116 grammes.
Original temperature of substance in heater 92° C.
Final temperature of "mixture" 22° C.
The water equivalent of the calorimeter
= 45 X 0-094 = 4-2 grammes.
102 Meamirement of Heat [CH.
Therefore the total equivalent mass of water
= 132 + 4-2 - 136-2 grammes.
Therefore the heat received
= 136-2 X (22'- 15) = 953-4 units.
Now this heat must have been given out by 116
grammes of substance cooling from 92° to 22°, that is,
through 70°.
Therefore the heat which would be given out "by
1 gramme cooling through 1°
= ,?«--, = <>••''■
116 X 7
Therefore the specific heat of the substance = 0-117.
In all heat measurements our results are determined
from the following fact :
Heat received by calorimeter and water = heat given
by substance inserted.
There is no need for us to express any of this as
mathematical formulae. The fundamental ideas are
quite simple, and the examples can be and should be
worked out from first principles.
Calorific value of fuels. It is often very important
that engineers should know how much heat is given by
burning a known quantity of different kinds of fuel.
As we have said before we buy fuel for the heat energy
which we can get out of it, and the cheapest fuel is
that w^hich will give the greatest amount of heat for
every shilling which we pay for it.
The number of heat units per unit of mass of fuel is
called the calorific value of that fuel.
One of the methods of determining this value is by
the use of the Darling calorimeter, the main ideas of
which are illustrated by Fig. 37,
IX]
Measurement of Heat
103
A known mass of the fuel is placed in a small
crucible C which is placed inside a bell jar B. This
jar is fastened down to a special base plate. The
products of combustion can only leave the jar through
the outlet at the bottom of the base-plate, and this
outlet R is like a watering-can rose with very fine holes.
A supply of oxygen — which, of course, is necessary for
the combustion of the fuel — is admitted at the top of
Oxygen
inlet
Fia;. 37
the bell jar and its rate can be regulated by means of
a regulator.
The bell jar and its attachments thus form a small
furnace and this is immersed in an outer vessel containing
a known quantity of water at a known temperature.
104 Meatturemi'ut of Iddt [oh.
The fuel is then ignited (this being done by means of
a small piece of platinum wire heated by an electric
curi^nt) and the flow of oxygen is regulated so that
the "flue gases" formed by the burning fuel bubble
slowly up through the water. Thus they give out their
heat to the water.
When the fuel has completely burned itself out the
water is allowed to flow inside the jar so that we can
be quite sure that all the heat generated has been
absorbed by the water. The temperature is then taken
and the calorific value is calculated as shewn below.
Mass of water = Mw lbs.
Water equivalent of calorimeter: Bell-jar, etc.
= Mc lbs.
(This water equivalent is usually given by the makers
of the calorimeter, but of course it can be calculated or
determined by experiment. In this case a record would
be kept for future use.)
Total equivalent mass of water = Mw + Mc = M lbs.
Original temperature of water = t° F.
Final temperature of water after fuel has been
burned = t° F.
Therefore heat received by water = M x (ig — ^i) b.th.u.
Mass of fuel burned = P lbs.
Therefore if M {t^ — tj) b.th.u. were given by the
combustion of P lbs. — ^A, — - British thermal units
would be given by 1 lb. in burning.
And this is the calorific value of the fuel.
The results could all be taken with metric units, if
desired, and the calorific value in calories per gramme
could be determined.
IX j Measurement of Heat 105
The following table shews the calorific values of
some fuels in British thermal units per lb. of fuel.
Methylated alcohol
11,320
Steam coal
15,600
Benzol
17,750
Bituminous coal
14,600
Petrol
20,000
Coal gas (London)
500 B.TH.U.
Paraffin oil
19,000
per cubic foot
Two values for the Specific Heat of a Gas. The
reader has already noted that two values are quoted
on page 98 for the specific heat of air. It has been
found that if the volume is kept constant the gas ab-
sorbs less heat per degree of temperature than it does if
it is allowed to expand at constant pressure. This is an
interesting and important matter to engineers. The
explanation is to be found in the fact that if the gas
expands it has to do work in pushing back the surround-
ing atmosphere, just as if it were pushing back a piston
in an engine cylinder. This work is done at the expense
of some of the heat which is being given to it and there-
fore we have to give it more heat to raise its temperature
through each degree than would be necessary if it was
not expanding. The additional heat represents the
work which the gas is doing in -expanding.
The methods for the determination of these specific
heats are of a very refined order, and the details cannot
be dealt with in this little volume.
106 M(<if<i(i< iiif III ill' Ilfttf [<n. IX
EXAMPLES
1. Find the heat necessary to raise the temperature of 3-5 lbs.
of water from 59° F. to 212° F. If the same amount of heat be given
to 17-5 lbs. of iron at 59° F. to what temperature would it be raised ?
The specific heat of iron = 0-1 12/
2. 4-8 lbs. of copper at 177° F. are plunged in 3 lbs. of water at
60° F. and the resulting temperature of the mixture is 75-6° F.
What is the specific heat of the copper?
3. A copper calorimeter (sp. heat -094) weighs 0*2 lb. and
contains 0-75 lb. of water at 50° F. What is the water equivalent
of the calorimeter and the total equivalent weight of water of
calorimeter and contents? It is found that when 2-5 lbs. of iron
at some unknown temperature are placed in the calorimeter the
temperature rises to 60° F. How much heat did the iron give out
and what must its original temperature have been? Sp. heat dl
iron -3 01 12.
4. If all the heat given by 0-02 lb. of coal of calorific value
15,600 B.TH.u. per lb. were given to a glass vessel containing 3 lbs.
of water at 60° F. (the glass vessel weighing 2-7 lbs. and having a
specific heat of 0-19) to what temperature would it be raised?
5. A mass of 200 grammes of copper of specific heat 0-1 is
heated to 100° C. and placed in 100 grammes of alcohol at 8° C.
contained in a copper calorimeter of 25 grammes mass : the tem-
perature rises to 28° C. What is the specific heat of the alcohol ?
6. 3-5 lbs. of water at 200° F. are mixed with 5 lbs. of water
at 60° F. the cold water being poured into the hot which is con-
tained in a copper calorimeter of 1 lb. weight and specific heat 0-1.
Find the temperature of the mixture (a) neglecting the calorimeter,
(6) taking the calorimeter into account.
CHAPTER X
FUSION AND SOLIDIFICATION
The third important effect of heat upon matter is
that known as a change of physical condition such, for
example, as the change of a substance from the sohd to
the Hquid form. If such a change is effected without
producing any change in the chemical constitution of the
substance it is called a physical cJiange of state. When
heat is given to ice it changes to water (which is
chemically the same thing) and if more heat be given
it will ultimately change again to steam, which again
has the same chemical composition.
When heat is applied to coal chemical changes take
place, and the same applies to many other substances.
But if no chemical change is produced then the physical
change is produced : and we shall only consider such
change in this volume.
Melting Point of a Solid. The temperature at which
a solid melts — that is to say changes into the liquid
form — is called the melting point of that solid. Different
substances have different melting points as the following
table shews.
Iron (wrought) 1600° C.
Ice
0°C.
Aluminium
600
Antimony
Bismuth ...
440
26.5
Brass
1015
Carbon . . .
3500
Copper . . .
Gold
1050
1250
Iridium . . .
1950
Iron (cast) ..
1100
Lead
325
Mercury
. - 39-5
Platinum . .
. 1700
Silver
. 1000
Steel
. 1350
Tin
. 231
Tungsten . .
. 3200
Zinc
. 420
!()}{ Fusion it 11(1 Solidification [CH.
The melting point is usually a well-defined tempera-
ture though there are some substances like glasg, for
example, which become plastic and slowly change to
the fluid state. It is difficult to determine the exact
melting point of such a substance.
The solidifying point or freezing point of a liquid is
that temperature at which it changes from liquid to
soUd. This temperature is the same as the melting
point. That is to say, ice melts at 0° C. and water
freezes at 0° C.
Heat required to melt a solid. In order to melt a
soHd it is not enough to heat it to its melting point.
Additional heat must be given when this temperature
is reached and it will be found that such heat does not
produce any increase in temperature until the whole of
the soUd is melted. If some ice be placed in a vessel and
the vessel be heated over a furnace it will be found that
(a) the temperature of ice will increase if it were
below 0° C. at the start :
(6) when it reaches 0° C. it will remain stationary
until every particle of ice is melted :
(c) when the ice is all melted then the temperature
of the water will rise.
During this experiment the ice and water must be
kept thoroughly stirred.
The same thing exactly applies to the melting of
any other substance though equal masses of different
substances do not all require the same quantity of heat
energy to melt them after the melting point has been
reached. In this respect ice requires more heat than
is required by any of the metals given in the above
list. The reader must think this over carefully and
see that he understands exactly what is meant.
x] Fusion and Solidification 109
Latent Heat of Fusion. The quantity of heat
necessary to change a unit mass of a solid at its melting
POINT to liquid at the same temperature is called the
latent heat of fusion of that substance.
For example the latent heat of fusion of ice (on the
British system of measurements) is 144. That is to
say 144 b.th.u. of heat are required to change
1 lb. of ice at 32° F. into 1 lb. of water at 32° F.
Conversely when 1 lb. of water at 32° F. freezes to ice
at the same temperature it must give up 144 b.th.u.
of heat.
On the metric system the quantity of heat necessary
to melt 1 gramme of ice at 0" C. and change it to water
at 0° C. is 80 calories.
The latent heat of fusion of a few substances is
shewn below.
Latent heat in British thermal units per lb. of
substance.
Ice ...
144
Bismuth
23
Zinc ...
i51
Sulphur
17
Silver
38
Lead . . .
9-6
Tin ...
25-6
Mercury
5
- An interesting experiment, which illustrates how
melting points may be determined and demonstrates
at the same time the fact that heat is absorbed or
yielded by a substance in changing its physical state,
may be performed by placing some paraffin wax, or better
still some naphthalene, in a boiling tube and heating
this tube in a water bath. The bath should be
heated until all the wax has melted. A thermometer
should then be placed in the hquid formed and the
bath allowed to cool. Readings of the thermometer
110
Fiution and Solidiji cation
[CH.
should then be taken at regular intervals of time — say
every half-minute. It will be noted that the thermo-
meter falls steadily to a certain "temperature after which
it remains stationary (or in some cases it may even
rise again slightly) for several minutes. During this
stationary period it will be noted that the wax is
solidifying, and when it has all become solid the tem-
perature will start to fall again.
Fig. 38 gives two graphs (one for wax and the other
for naphthalene) shewing how the temperature falls with
90
80
70
V
\
\
\
■
\
0
y
\
\
\
\^
\
<^
\
N
v/
:^
k
\
\
^\
^-7v
\
^
^t(
^
X'
\^\
^
^
^
2 4 6 8
10
Mini
12
ites
14
16
18
20 22 24
Vm.
38
the time. The melting point is that temperature at which
the cooUng temporarily ceases. The explanation lies in
the fact that on solidifying the substance gives out heat,
and this heat suffices to prevent the temperature from
falling. In the case of substances with a more defined
melting point than wax the heat given out on soUdifi-
cation will cause the temperature to increase. This is
shewn on the naphthalene graph. It should be pointed
x] Fusion and Solidification 111
out that the melting point of the naphthalene is given
by the horizontal part of the graph.
We may also compare, roughly, the latent heat of
each substance by noting the length of time during
which the temperature remains practically constant.
The longer the time the greater must be the quantity
of heat given out. Of course, the reader will see that
such comparison could only be made if equal masses of
substances were used and allowed to cool under equal
conditions. This in turn would mean that only sub-
stances with approximately equal melting points could
be compared in this way. From our curves we can see
that the naphthalene has a greater latent heat than the
wax.
Change of volume with change of state. It is found
that some substances, like water, increase in volume in
passing from the hquid to the solid state. That is to
say a given mass of the substance will have a greater
volume in the solid state than in the liquid state at the
same temperature. We say that such substances expand
on solidification. Other substances contract on solidifi-
cation.
This is important to engineers for many reasons.
Firstly, whenever a casting is made we have a liquid
changing to solid. If that substance contracts on
solidification the chances are that we shall not be able
to get a good casting- — that is to say a well defined
casting — because the metal will shrink away from the
sand mould. If we can use a metal which expands
slightly on solidification, or one which does not change
in volum.e, we shall get sharp castings which will not
need so much machining. Metals like copper and iron
contract on solidification. Antimony and bismuth
112 Ftmon ami Solidificafion [CH.
expand on solidification. Some alloys like type-metal
(an alloy of lead, tin and antimony) expand on solidifi-
cation. In fact that is the sole reason why this par-
ticular alloy is used for making type. Some readers
may have seen castings which were ready for immediate
assembling on being taken out of the sand. They are
sharply defined, have smooth surfaces, and do not
require any machining.
Secondly, if there is going to be any appreciable
change of volume then account will have to be taken
of this in the size of the pattern. The volume of the
pattern will be the volume of the molten metal.
Again, especially in the case of larger castings, the
metal nearer to the sand will solidify first, so that when
the inner portions sofidify stresses are produced due to
internal contractions or expansions, and these may
cause the casting to break.
It is well known that water expands on sofidification.
Water pipes are burst in winter time by that expansion.
It is that same expansion which breaks up the soil for
the farmer.
Determination of the Latent Heat of Fusion of ice.
A calorimeter, of known water equivalent, containing
a known mass of water at a known temperature is
taken, and into this are dropped small pieces of dry
ice (each piece must be carefully dried with flannel).
This process is continued until the temperature of
water has been reduced several degrees and when all
the pieces of ice which have been introduced are seen
to be melted the temperature is taken. The calorimeter
and its contents are weighed again so that the mass -of
ice which has been melted may be determined. From
this the latent heat may be calculated.
x] Fusion and Solidification 113
The heat given out = (total equivalent mass of
water) x (fall in its temperature).
The heat received = (mass of ice x latent heat of
fusion) + (mass of . ice x rise in temperature from
melting point to final temperature).
It will be seen that unless the temperature of the
water is reduced to the melting point then the ice will
receive heat firstly to melt it and secondly to heat the
melted ice up to the final temperature of the water in
the calorimeter.
Since the heat received = heat given out,
the latent heat is easily determined.
In performing the experiment it is well to start with
the temperature of the water a few degrees above and
to stop adding ice when it is the same number of degrees
below the temperature of the room. The pieces of ice
should be small and clean, and they should not be
touched by the naked fingers.
Solution: Freezing mixtures. Whenever a solid
dissolves in a liquid without producing any kind of
chemical change the temperature of the liquid is
reduced. A chemical change always generates heat :
and thus when a solid is dissolved in a liquid and pro-
duces a chemical combination the liquid will be heated
if the chemical change is greater than the physical
change and vice versa.
A mixture of salt and pounded ice or snow falls to
a temperature as low as — 22° C. or — 7-6° F., according
to the proportions of ice and salt.
Effect of Pressure on the Melting Point. The
temperature at which a solid melts is only slightly
affected by pressure. Ordinary changes in atmospheric
pressure do not produce any measurable effect upon
V. Y, 8
114 i'nsiiui iind So/if/t/ica/ ioti |('H, X
the melting point, but it greater pressures be applied it
is found that
(a) substances which expand on solidification have
their melting points lowered by an increase in pressure,
and
(6) substances which contract on solidification have
their melting points raised by an increase in pressure.
That is to say ice can be melted by the application
of great pressure, but of course the water so formed will
be below the temperature of the freezing point and will
freeze again at once when the pressure is released.
The making of a snowball ; the freezing together of
two coUiding icebergs ; the progress of glaciers, are all
explained by this.
EXAMPLES
1. How much heat would be necessary to heat up 3 lbs. of ice
from a temperature of 10° F. to its melting point, to melt it, and to
heat the water to the boiling point ? The specific heat of ice is 0-5
and its latent heat is 144 on the BritLsh system.
2. Compare the quantities of heat necessary to melt 4 lbs. of
each of the following substances assuming thai they are all at' 32° F.
to start with : ice, silver and lead. See pages 107 and 109 for melting
points and latent heats, and page 98 for specific heats.
3. A cavity is made in a large block of ice and into it is put
an iron sphere at a temperature of 1000° F. The iron weighs
0-64 lb. and its specific heat is 0-112. How much water will be
formed in the cavity?
4. How many heat units on the c.g.s. system would be given
out by half a litre of water in cooling down from 15° C. and freezing
at 0° C. ? If this heat were given to 1 lb. of lead at 15° C. to what
temperature would it be raised ? (Melting point, 325° C. : specific
heat, 031 : latent heat, 9-6.)
CHAPTER XI
VAPORISATION
Just as a solid may be changed to the Hquid form
by the apphcation of heat so can a hquid be changed
to the gaseous form. This change of physical state is
called vaporisation, the reverse change (from gas to
liquid) being called condensation.
Vaporisation can take place either by the process
known as evaporation or by the process of boiling or
ebullition. These processes differ from one another.
Evaporation takes place at all temperatures but it
only takes place from the surface of a liquid. If equal
quantities of water are placed in different vessels — one
an open shallow dish, the other a tall narrow flower
vase, for example — and left over night in the same
room after having been weighed, it will be found next
morning that the shallow vessel has lost more weight
than the other one. We all know how a cork in a
bottle will prevent evaporation : how an imperfect cork
is a useless thing in a scent or other spirit bottle.
Ebullition or boiling will only take place at one
definite temperature for a given liquid at a given pressure,
and it takes place throughout the whole mass of the
Uquid.
Boiling Point. We will deal with ebullition first.
A hquid is said to be boifing when bubbles of vapour
8—2
IIU VnjHfn'siifioii [CH.
fomied at the bottom of the vessel rise up throughout
the mass of the hquid and "burst" into tlie space
above. Such bul)bles must not be confused with the
more minute air bubbles which may rise up as soon as
heat is supplied.
As soon as the liquid commences to boil its tempera-
ture tvill cease to rise. The temperature of the hquid
when this happens will be the boiUng point of that
liquid : the temperature of the vapour in the space
above will be the boihng point of that liquid which
is formed by the condensation of the vapour. For
example, if we boil some salt water we shall find that
the temperature of the hquid is higher than that of the
vapour above it. As we know, the vapour is steam
and it will condense to water. Therefore the tempera-
ture of the vapour is the boiling point of water: but
the temperature of the hquid is the boiling point of
that particular sample of salt water.
As a general rule if the hquid is of the same chemical
composition as the vapour above it we take the tem-
perature of the vapour, because the boiling point of a
hquid is shghtly affected by mechanical impurities and
by the material of the containing vessel.
Effect of Pressure on the Boiling Point. If we test
the boiling point of a hquid on different days we shall
find that it varies and that it is sHghtly higher when
the barometer is higher. This suggests that the
boiling point is affected by pressure. Complete in-
vestigation leads to the discovery that a given hquid
may be made to boil at any temperature within wide
limits and that an increase in pressure raises the boiling
point of all liquids whilst a decrease in pressure lowers
the boihng point.
I
XI]
Vaporisation
117
The reader naturally enquires what is the boiling
point of a Uquid? The answer is that we must define
the boiling point of a given liquid as the temperature
at which it boils at some definite pressure, and that the
boiling points of all liquids should be taken at that
pressure. The pressure chosen for this purpose is the
normal atmospheric pressure- — that is to say the pres-
sure of the atmosphere when the barometric height is
30 inches of mercury. This pressure is sometimes
called a pressure of 1 atmosphere and is equivalent
to 14-7 lbs. per square inch. Thus the boiling point
of water is 100° C. or 212° F. when it is boiled in a
vessel open to the atmosphere and the barometer
stands at 30 inches.
If the water be boiled in a vessel which can be closed
- — like the boiler shewn in
Fig. 39— it will be found
that, as the steam pressure
inside increases, the boiling
point will rise as shewn by
the thermometer. The pres-
sure can be determined by
means of a pressure gauge,
either of a direct reading
pattern or of the pattern
shewn in the figure. This
is a U-tube having fairly
long limbs. Mercury is put
into this and when it has the
same level in each limb then
the pressure of the steam
must be equal to that of the atmosphere. As the steam
pressure increases the mercury will be forced down the
Fig. 39
118
VaporisaUon
[CH.
left and up the right limb and the steam pressure will
then be greater than the atmospheric pressure by an
amount represented by the difference in level of the
mercury in each hmb. That is to say, if the difference is
6 inches and the atmospheric pressure is 30 inches then
the steam pressure must be equivalent to that produced
by a 36 inch column of mercury. Thus the relationship
between the pressure of the steam and its temperature
can be determined within the ranges possible with the
apparatus.
Fig. 40 is an illustration of a converse experiment.
It shews how water may boil
at a lower temperature than
100° C. by reducing the pressure
upon it. Some water is put
into a round-bottomed flask
and boiled. When it is boiling
and steam is issuing freely we
know that all the air has been
driven out of the flask. The
flame is removed and a cork
with a thermometer is fitted.
Then some cold water is
squeezed out of a sponge on
to the flask and it is noticed
that the water inside at once ^'J^- *^
begins to boil again. The colder the water in the
sponge the more vigorous will be the boihng of the water
inside the flask, but of course the thermometer will
indicate a rapidly falling temperature.
Obviously the cold water will cause some of the
steam inside to condense : this condensation will reduce
the pressure : this reduction will lower the boiling point
Hi=
^^ 1
XI]
Vaporisation
119
and the water will boil. There is always the risk of
the flask breaking in this experiment, and it should be
made of good quality glass, and of the shape shewn.
Temperature of steam at different pressures. The
graph shewn as Fig. 41 indicates the temperature of
400
350
300
250
200
,-^
^
/
/
/
/
/
100
0
5
0 K
)0 1
50 2(
)0 2>
30 3C
0
Pressure in lbs. per sq. inch
Fig. 41
steam at various pressures. At atmospheric pressure,
14-7 lbs. per square inch, the temperature of the steam
is 212° F. At a pressure of 150 lbs. per square inch it
is 358° F. : at 200 lbs. per square inch it is 381° F. and
1 20 Vaporisation [oh.
at 300 lbs. pressure it is 417° F. The average working
steam pressures lie between 150 and 200 lbs. per square
inch. Since the relationship between pressure and
temperature can be obtained from the above graph,
and since the relationship between the height of a place
above sea level and the atmospheric pressure at that
place compared with sea level pressure can also be
obtained from a similar graph, it is quite obvious that
height above sea level may be measured by finding the
boiling point of water at various heights.
Evaporation. As we have said before this process
goes on at all temperatures but only from the surface
of a liquid. Our common experiences have taught us
that some liquids evaporate much more quickly than
others. We all know that petrol, scent, alcohol and
benzoline will evaporate very quickly indeed, and
we know the necessity for well-fitted stoppers for the
vessels containing such liquids. We also know from our
own experiences how water will evaporate or dry up
more quickly on some days than on others. We know
too that it is not entirely a question of temperature.
We can think of hot close days in summer when water
will not dry up at all. On such days the atmosphere is
said to be saturated with water vapour : it cannot hold
any more, and consequently no more evaporation of
water can take place. That will not affect the evapora-
tion of other liquids : but if the atmosphere could
become saturated with petrol vapour (we hope that it
never will) then even petrol would cease to evaporate.
That indeed is the secret of the cork in a bottle. The
space in a bottle jibove the liquid soon becomes satu-
rated ; and then the liquid cannot evaporate any more :
but if there were no cork to the bottle then the vapour
XI J Vaporisation 121
would go out into the atmosphere in a vain attempt
to saturate that.
Heat necessary for Evaporation. Although this
process goes on quietly and at all temperatures yet heat
is necessary for its accomplishment. If a little alcohol,
or petrol, or, better still, ether be poured on to the hand
a sensation of cold will be experienced. Yet if the tem-
perature of the liquid be taken it will be found to be
the same as that of the room in which it is. The
sensation of cold is brought about by the fact that the
liquid absorbs heat more or less rapidly from the hand
in proportion to its rate of evaporation. Thus the
ether will feel colder than the alcohol, which in turn
will feel colder than water — though in fact all three will
have practically the same temperature*.
The rate at which they evaporate depends upon
their boiling point and upon the condition of the space
above them. A liquid with a low boiling point will
evaporate much more quickly than one with a high
boiling point — other things being equal. Nevertheless
the liquid will require heat and the greater its rate of
evaporation the more heat it will need. Some readers
may have been unfortunate enough to have had their
gums frozen prior to a tooth extraction. The "freezing "
is produced by the rapid evaporation of ether absorbing
much heat from the gum.
The cooling effect produced by "fanning" the face
is due to the fact that the fan is continually replacing
* When a liquid evaporates the portion of liquid remaining
will generally have its temperature diminished. How much it is
diminished will ' depend upon the quantity of liquid, the rate of
evaporation and the rate at which it receives heat from external
sources.
122 Vaj)orisafi(Hi [vH.
the air near to the face with comparatively fresh and
unsaturated air so that evaporation of the moisture on
the face can proceed more rapidly. This evaporation
can only take place by absorbing heat from the face :
hence the coohng sensation. The same thing applies
to the common method of finding which way the wind
blows : that is by holding a moistened finger in various
directions. That direction in which it feels coldest is
the direqtion from which the wind is proceeding.
Vapour Pressure. Every kind of vapour exerts
some pressure. The pressure which it exerts depends
upon the amount of vapour present and upon the
temperature. If the temperature is constant then as
more and more liquid evaporates the pressure of the
vapour will increase until the space is saturated with
that vapour. Thus it follows that at a given tempera-
ture a particular vapour will exert a maximum pressure
when the space is saturated.
But though a space may be saturated with one
vapour it can hold other vapours. And the total
pressure in any enclosed space will be the sum of all
the pressures produced by the several vapours. (This
is known as Dalton's law but it is only approximately
true in most cases.)
If a space be saturated %ith vapour and the tem-
perature be increased it will be found that the pressure
increases — though not proportionately. It will also be
found that when the vapour pressure is equal to that
produced by 3.0 inches of mercury the temperature will
be the boiling point of that substance.
And from this it has been shewn that a liquid will
boil whenever the pressure acting upon it is equal to
its saturated vapour pressure. Therefore we can boil
xi] Vaporisation 123
a liquid at any temperature provided that we can
adjust the pressure upon it to equal that of its saturated
vapour pressure at that temperature. The boiling
point of a liquid may therefore be defined as that
temperature at which its vapour pressure is equal to
that of 30 inches of mercury.
Boyle's Law and Vapour Pressure. If a saturated
vapour occupies a definite volume and we reduce the
volume, then if Boyle's law were to hold good the
pressure of the vapour would be increased thereby.
Actually however nothing of the kind occurs. The
saturated vapour pressure cannot be increased except
by an increase of temperature. We find on reducing
the volume that some of the vapour condenses : but
the pressure remains the same. Boyle's law does not
hold good !
An experiment was performed by Dalton to illus-
trate this. He made an ordinary mercury barometer
using a longer tube than usual and a longer cistern
(Fig. 4:2, A). Then he introduced a drop of ether into
the tube by means of a bent pipette. This rose to the
top and immediately evaporated, the pressure of the
vapour causing the mercury to fall a little (B). Then he
introduced a little more ether and a further fall of the
mercury resulted. . So he continued until he noticed
that the ether ceased to evaporate, shewn by the
appearance of a layer of ether Uquid on the top of the
mercury (C). He then found that the introduction of
more ether did not increase the pressure — the liiercury
remained at the same height — but simply added to the
quantity of ether liquid floating on top of the mercury.
Then he lowered the barometer down into the cistern
{D and E) thereby diminishing the volume of the space
Vnporixdt'um
[CH.
above the mercurv, but he found that the pressure was
not alt<>red — shewn by tlie mercury remaining at the
same level. At the same time he noticed that the
quantity of liquid ether above the mercury increased.
Then he gradually withdrew the tube out of the cistern
so increasing the volume of the space above the mercury.
Fig. 42
But again he found that the pressure remained constant
and that the quantity of liquid ether diminished. When
he was able, to get the tube high enough so that all the
liquid ether had disappeared {F) then he found a slight
drop in pressure shewn by the mercury rising [O).
He thus found that so long as a space is saturated
with vapour that vapour will not obey Boyle's law :
XI J Vajjorisation 125
that no change in pressure could be produced by altering
the volume of the space so long as the space was saturated.
He also found by further experiment that Boyle's law
does not hold good even when a space is not saturated ;
but that the further the space is from saturation the
closer does it follow the law.
Temperature and Vapour Pressure. An increase in
temperature will cause an increase in pressure in either
a saturated or an unsaturated space.
If a space be unsaturated a decrease in temperature
will also cause a decrease in pressure, but if the tempera-
ture be lowered sufficiently (depending upon the vapour
under experiment) the space will become saturated and
some of the vapour will condense : but the pressure
will decrease so long as the temperature is decreased.
Charles' law does not hold good : but it is approxi-
mately true in the case of non-saturated spaces ; and
the further the space is from saturation the closer does
that space obey the law.
Latent Heat of Vaporisation. Heat is necessary to
vaporise a liquid whether the process of vaporisation is
that of evaporation or of ebullition. The number of
units of heat required to change a unit mass of a liquid
into the gaseous state without a change in temperature is
called the latent heat of vaporisation of that liquid.
It has been found that this is not a constant quantity
for a given substance : it depends upon the temperature
at which vaporisation takes place. However, it is usual
to speak of the latent heat of vaporisation of a substance
as the quayitity of heat necessary to clmnge a unit mass of
the liquid at its normal boiling point to vapour at the same
temperature.
We are chiefly concerned with water and steam.
126 Voporisaffo)f [ch.
The latent heat of vaporisation oi uatei' — more com-
monly called the latent heat of steam — is 066 British
thermal units per pound, or 537 calories per gramme.
This means that in order to change 1 lb. of water
at 212° F. into 1 lb. of steam at 212° F. we have to
supply 966 British thermal units of heat. Conversely
when 1 lb. of steam at 212° F. condenses to water at
the same temperature it gives out 966 British thermal
units.
Sensible Heat and Total Heat. If we have 1 lb. of
water at 60° F. and we wish to convert it to steam at
atmospheric pressure we shall have to give it heat
(1) to raise its temperature from 60° F. to 212° F. and
(2) to convert it from water at 212° F. to steam at
212° F.
For this we shall require (1) (212 — 60) x 1 units,
and (2) 966 x 1 units, that is to say 1118 units in all.
The heat which produces a change in temperature
is often called the sensible heat. In the case just
quoted the sensible heat amounts to 152 units. The
sum of the sensible heat and the latent heat is called
the total heat.
Determination of the Latent Heat of Steam. In this
measurement it is necessary to pass a known mass of
dry steam into a calorimeter of known water equivalent
containing a known mass of water at a known tempera-
ture. This steam will heact the water and from the
increase in temperature we can easily find how much
heat the water and the calorimeter have received. Now
all this must have been given out by the steam and it
gave it (a) in condensing, (6) in cooling down from water
at the boiling point to water at the final temperature of
the calorimeter. As we can easily calculate this latter
xi] Vajmrisatio^i 127
amount, we have only to subtract it from the total
heat received by the calorimeter and the remainder
must represent the heat given out by the steam in
condensing without change in temperature. We can
then calculate how much a unit mass of steam would
have given out and the latent heat of steam is deter-
mined.
The usual method is as follows :
Weigh the inner vessel of the calorimeter.
Partially fill with water and weigh again.
From this get the weight of the water.
^ Add to this the water equivalent of the calorimeter.
Take the temperature of the water.
Then allow dry steam to pass into the water.
When the temperature of the water has risen some
20 degrees shut off the steam, stir well, and take the
final temperature of the water in the calorimeter.
Weigh again so that you may get the mass of the
steam condensed.
Calculate the value of the latent heat of steam.
The chief points of importance in the performance
of this experiment are (a) to be sure that the steam
which is passed into the calorimeter is quite dry and
does not carry any water particles with it ; and (6) to
prevent loss of heat due to radiation from the calori-
meter. The steam may be made dry by using some kind
of a steam dryer such as that shewn in Fig. 43. The
loss of heat can be reduced to a minimum by arranging
that the temperature of the water in the calorimeter
shall be as much below the temperature of the room
at the beginning of the experiment as it is above it
at the end. Thus the loss and gain of heat will approxi-
mately balance.
\'2i\
Viijutnsntitnt
[CH.
There is nothing difficult about the calculations.
The only point which is likely to be overlooked is that
the heat given out by each unit mass of steam in con-
densing down to the final temperature is the total heat,
and that this is the sum of the sensible heat and the
latent heat.
Steam
entry
Exhaust ^
for condensed
water
Steam exit
to Calorimeter
Fig. 43
Variation of Latent Heat of Steam with Temperature.
Regnault fovmd that the latent heat of steam was not
a constant quantity. He found that as the tempera-
ture at which the steam is produced increases (due to
increased pressure upon the water) the latent heat
decreases and vice versa.
It has been shewn that the variation is approxi-
mately as follows: for each degree F. above the
boiling point (212°) the latent heat of steam is dimin-
ished by 0-695 b.th.u. per lb. of steam, and for each
degree F. below the boiling point the latent heat is
increased by 0-695 b.th.u.. per lb. of steam.
xi] Vaporisation 129
Thus at a temperature of 300° F. the latent heat of
steam will be 966 less 0-695 unit for each degree above
212°. That is to say the latent heat will be
966 - (88 X 0-695) - 966 - 61-16 = 904-84-
Similarly at a temperature of 180° F. (that is under
reduced pressure) the latent heat of steam would be
966 + {(212 - 180) X 0-695} = 988-24.
On the metric system of units the variation is
0-695 calorie per gramme for each degree Centigrade
above or below the boiling point (100° C).
Pressure and Temperature of Saturated Steam.
Although we know that an increase in pressure
causes an increase in temperature of the steam above
boiling water yet no definite law connecting these
quantities has been expressed. Certain empirical
formulae have been deduced to enable one to calculate
the pressure at some known temperature or vice versa,
and these formulae are often used for the purpose.
It is more usual, however, for engineers to use tables
which have been drawn up from the formulae. These
tables shew at a glance the value of the pressuie
for any temperature. The graph shewn in Fig. 41 is
plotted from such a table.
Pressure and Volume of Saturated Steam. Again
there is no simple law connecting the pressure and the
volume of saturated steam. This will be discussed
again in the chapter on Thermo -dynamics.
Hygrometry. Hygrometry is the measurement of
the amoimt of water vapour present in the air. The
actual amount of water vapour present in a given mass
of air is called the absolute humidity of that air. This is
determined by passing a known volume of the air
through some previously weighed tubes containing
p.y. 9
130 Vaporisation [CH.
some substance (like calcium chloride) which will
readily absorb all the water vapour. The tubes are
again weighed and the increase represents the amount
of water vapour which was present in that particular
sample of air.
The absolute humidity of the air varies from day to
day. But so far as our sensations are concerned we
may easily be led into errors in this respect. In the
early morning or after sunset we might assume that
there is more vapour in the air than at noon, whereas
the converse might be true. Or in other words it does
not follow that, because the air is saturated on one
occasion and not on another, the actual amount of
vapour present is greater.
When the air feels "dry" more vapour is necessary
to saturate it. When it feels "moist" it is saturated
or nearly saturated. Further when the temperature is
high more vapour will' be necessary to produce satura-
tion than when it is low. Thus it is quite possible that
the absolute humidity on an apparently "dry" day in
summer is greater than on an apparently "moist" day
in winter.
The ratio of the quantity of water vapour actually
present in a given volume of air to the quantity which
would be necessary to produce saturation at the same
temperature is called the relative humidity.
Thus when the relative humidity is 1 the air is
saturated and the smaller the relative humidity the
further is the air from saturation.
The Dew-point. The temperature at which the
amount of vapour actually present would produce
saturation if a volume of the air were cooled at constant
pressure is called the dew-point. This temperature will
xi] Vaporisation 131
always be lower than the air temperature unless the
air be saturated or supersaturated, in which case rain
will be falHng. Dew may be regarded as "local" rain:
the word local being used to indicate the immediate
neighbourhood of blades of grass, etc., which become
very cold at night due to excessive radiation of heat
(see p. 148).
Instruments used to determine the dew-point are
called Hygrometers. There are several different forms
and the principle consists in cooling d(5wn some surtace
to which a thermometer is thermally connected until
a film of dew appears. The temperature is read, and
the cooling process discontinued. When the film dis-
appears again the temperature is read again and the
mean of these readings is the dew-point.
So far as the dew-point of the atmosphere is con-
cerned these readings must be taken out of doors, other-
wise the dew-point found is simply that of the air in the
room in which the experiment was performed and this
would afford no index of the atmospheric conditions.
The wet and dry bulb hygrometer is very commonly
used though its users do not bother as a rule to find
the dew-point. The instrument consists of two similar
thermometers placed side by side. One of these has
some musHn round its bulb and some cotton wick
attached to this muslin dips into a vessel of water.
The water runs up the wick and so keeps the muslin
moist. This moisture evaporates, absorbing heat from
the thermometer which therefore records a lower
temperature than the dry bulb thermometer. Clearly
the lower the dew-point the more rapid will be the
evaporation of the water on the muslin and the lower
will be the wet bulb thermometer reading. This
9—2
132 Vupoi'imtwa [CH. XI
reading is not the dew-point: but tables have been
drawn up by means of which the dew-point may be
obtained from the readings of the two thermometers.
This instrument is generally quoted in the daily
meteorological reports and the readings of the dry and
wet bulb thermometers are given. The man in the
street understands that if the difference of the readings
is great the air is dry and there is no immediate prospect
of rain ; whilst if the wet thermometer is nearly as
high as the dry thermometer he had better be provided
with an umbrella. For once in a way the man in the
street is on the right path.
EXAMPLES
1. 10 lbs. of steam at 212° F. are condensed into a large vat of
ice at 32° F. How much ice will be melted, assuming that the
temperature of the vat remains at 32° F. all the time ?
2. Steam is condensed by allowing it to pass through a large
length of coiled tube in a vessel containing 120 lbs. of water. The
original temperature of the water was 59° F. and after 15 minutes
it was found to be 130° F. : how much steam was condensed?
3. How much heat would be necessary to convert 12-5 lbs. of
ice at 32° F. to steam at 212° F.? Give the answer in British
thermal units and in calories.
4. If a boiler receives 120b.th. units of heat per minute through
every square yard of its surface, the total surface being 6 sq. yards,
and if its temperature be 280° ¥. while it is fed with feed water at
1 10° F., what weight of steam would you be able to dj*aw off regu-
larly per hour? (The latent heat of vaporisation at 280° may be
calculated as shewn at top of page 129.)
5. Steam is admitted into a water cooled condenser through
which 20 gallons flow per minute. The water on entering the con-
denser is at 60° F. and on leaving has a temperature of 100° F.
How much steam is being condensed per minute ?
CHAPTER XII
TRANSMISSION OF HEAT
There are three modes by which heat may be trans-
mitted from one point to another. The first is by
conduction and it is in this way that heat is transmitted
through soUds. If one end of a metal bar be heated
the other end will soon become hot provided that the
bar is not very long. The heat seems to pass from
molecule to molecule from the warmer end to the
colder end and will continue to pass so long as there
is any difference of temperature between the ends.
The process is comparatively slow : it is not to be
compared with the speed of light or sound or electricity,
or of heat transmitted by another process called
radiation.
Different substances conduct differently. In general
terms we all know that silver is the best conductor of
heat — -as it is of electricity — though it is quite possible
that most of us do not know quite what we mean when
we say it. One reader may be thinking that the heat
travels more rapidly along silver than along anything
else : another may be thinking that it is not so much
a question of speed as of quantity — that is to say that
more units of heat can pass at the same speed : another
may think that both speed and quantity must be taken
into account.
134 Transmission of Heat [ch.
If two equal rods of copper and bismuth be coated'
with wax and one end of each be put in a Bunsen flame
it will be found that the wax melts more quickly along
the bismuth at the start but ultimately more wax is
melted on the copper than on the bismuth bar.
The point of this experiment is that the specific
heat of the bismuth being less than that of the copper
a smaller quantity of heat is required to raise its
temperature. Thus its wax starts to melt before that
on the copper. But since more of the copper's wax is
melted ultimately it follows that at corresponding
points along each bar the temperature of the copper
was higher than that of the bismuth and that more
heat units per second were passing along the copper
bar than along the bismuth bar.
Thermal Conductivity. In order to compare con-
ductivities of different substances it will be necessary
to measure the quantity of heat which is transmitted
through equal distances, equal cross sectional areas, in
equal times and with equal differences of temperature
at the extremities of the equal distances.
The thermal conductivity of a substance is the
quantity of heat which passes in unit time through
a unit length having a unit cross sectional area when
the temperature at each end differs by one degree.
It is fairly evident that the quantity of heat whicli
will pass through any length will be directly proportional
to the difference in temperature at the ends, directly
proportional to the area of cross section, directly pro-
portional to the time and inversely proportional to
the length.
If the thermj^l conductivity of the substance be
known then the quantity of heat passing in any known
XIl]
Transmission of Heat
135
time, along any known length of known cross sectional
area with a known difference of temperature between
the ends may be calculated.
Conductivity of Wire Gauze. If a spiral of copper
or silver wire be placed over the wick of a lighted candle,
as in Fig. 44 (a), the flame will be extinguished at once
due to the fact that the copper conducts away the heat
so rapidly that the temperature is lowered below the
temperature of ignition. If however the spiral be
heated first and then placed over the lighted candle
wick the flame will not be extinguished.
Fig. 44
In the same way if a piece of fine wire gauze be
placed over a Bunsen burner, as in Fig. 44 (6), and if the
gas be lighted below the gauze it will be found that it
does not burn above the gauze. If the gauze be raised
and lowered it will be found that the flame rises and
falls with it. Of course gas is coming through the
gauze and this can be lighted in the ordinary way.
If the gas is extinguished and then turned on again
the gas can be lighted above the gauze and it will not
burn below. A yet more striking experiment is to
soak a piece of cotton-wool in alcohol and place it on
a piece of wire gauze. The gauze is then brought down
over a lighted flame and the alcohol will burn — but it
I'AG Tran»iniAmon of Heat [ch.
will only burn below tJie gauze, and if tlie piece of cotton
wool be picked up from the gauze "the flame" will not
come with it.
The explanations for all these simple experiments
lie in the fact that the gauze is a good conductor of heat :
that it conducts heat away rapidly in all directions over
its surface and having a large surface exposed to the air
keeps comparatively cool. Thus the temperature on
the other side of the gauze from that on which the flame
is playing is lower than the temperature of ignition of
gas or alcohol as the case may be.
Miner's Safety Lamp. It is generally known that
in most coal mines there is so much inflammable gas
evolved from the coal that the presence of a naked
flame would cause a disastrous explosion. The pro-
perty of wire gauze as shewn above was used by Sir
Humphry Davy in the design of a safety lamp for
use in such mines. The main idea of the lamp is that
the flame (a small oil flame) can only receive its supply
of air through some fine wire gauze, and further it is
surrounded by gauze.
Now although the inflammable gases may go in with
the air supply and burn inside the lamp yet the flame
cannot strike back through the gauze.
The lamp serves too as a danger signal. If there is
much gas burning inside the lamp the miner knows that
the proportion of inflammable gases is too great at that
place and he should immediately report the fact so that
better ventilation be secured.
Further, if the air is foiil the lamp will burn less
brightly and it may even go out altogether.
In most mines every lamp is lighted and tested, by
being lowered into a well of coal gas, before it is given to
XIl]
Transmission of Heat
137
the miner. It is also locked so that he cannot uncover
the flame.
Conduction in Liquids. With the exception of the
molten metals, liquids are comparatively bad con-
ductors of heat. Liquids are always heated from
below : we never think of putting the furnace at the
topmost part of a boiler. An experiment may be per-
formed in a manner shewn in Fig. 45, where we have,
a tall vessel of water with
a number of thermometers
projecting from it at various
depths. When some cold water
is put into this vessel all the
thermometers will read alike.
If a pan containing some
burning coals or some other
source of heat be applied to
the top of the water it will be
found that the various thermo-
meters are only very slightly
affected even after a consider-
able lapse of time. On the
other hand we know that if the source of heat be applied
to the bottom of the vessel the whole of the water will
become hotter in a comparatively short time.
We know also that if the same experiment were per-
formed with a solid block of metal there would be no
appreciable difference between top heating and bottom
heating.
Convection. When the water is heated at the
bottom the lower portion receiving heat expands and
therefore becomes lighter bulk for bulk than the water
above it. Consequently it rises, colder water descending
Fig. 45
138
Trmntmiasinn of Heat
[CH.
to take its place. This, in turn, is heated, expands,
becomes lighter and rises. In this way we get the
water circulating in the v-essel; warm and light water
continually rising whilst the cooler and heavier water
sinks to take its place. As the warm water rises it
gives out some of its heat to the surrounding colder
water. Thus we see that the particles of water move
•and all the upward moving particles are carrying and
distributing heat. This process of transmission of heat
is called convection and the currents of water set up are
termed convection currents.
This can be shewn very ejffectively by means of a
simple experiment illustrated in Fig. 46. A vessel of
^
- -y
W"
^^^rJMmr^-^
Fig. 46
water (this may be a flat lantern cell so that it can be
placed in a lantern and projected upon a screen) has
two thick wires leading down to a small coil of thin
wire at the bottom. Two or three crystals of potassium
permanganate are dropped down to this spiral and they
will dissolve colouring the water at the bottom.
A current of electricity is then passed through the
spiral which becomes warm. This warms the coloured
XIl]
Transmission of Heat
139
water which then rises and we can see the convection
currents by watching the paths of the coloured
streams, which follow the courses shewn by the
dotted lines in the diagram. The process will continue
until all the water is uniformly hot and uniformly
coloured.
This principle is the basis of heating by hot water
circulation. The circulation takes place quite naturally
and Fig. 47 illustrates a simple
system of such heating. The
boiler- — or more properly, heater
— is placed at the lowest part
of the building and the hot
water rises whilst the colder
water descends to take its place.
The method is sometimes called
central heating — that is to say
one fire will provide the heat for
all the rooms and corridors. The
system is often used in large
buildings, theatres, churches,
educational institutions and the
like, but is not often met with
in private houses in this country.
In America it is the general rule.
Its general efficiency, economy and cleanliness
deserve that it should meet with wider favour than it
does : though it seems highly probable that electric
heating will prove to be too strong a rival as soon as
electrical energy is more universally adopted.
Convection Currents in Gases. Gases are also bad
conductors of heat, and heat may be transmitted
through gases by convection. When heat is appHed
Fig. 47
140 Tninsiitlssiitii <>/ lleitt [CH.
to a gas the portion in the ininiediat^^ neighbourhood
of the source of heat expands, becomes hghter and
tends to rise. Since this expansion is greater than in
the case of Htjuids the convection current will be set
up much more quickly and it will move with a greater
velocity. The existence of these convection currents
is readily shewn in many ways.
In an ordinary dwelling room where there is a fire
the heated lighter air ascends the chimney. This is
useful in that it carries the smoke and soot : but it has
the serious drawback of carrying up a tremendous
proportion of the total heat energy of the fire.
This is one of the causes of the overall inefficiency
of steam engines : so much of the total energy of the
furnaces is carried up the flues by the air convection
currents.
From another point of view these flue convection
currents are useful for they assist in the promotion of
proper ventilation. If air is ascending the chimney
fresh air must be drawn into the room at the same rate.
This may come through special ventilator ducts, or
through open doors and windows, or — as is too often
the case — through the cracks and joints of imperfectly
fitting doors and windows. This fresh air is not only
necessary and beneficial to any occupants of the room
but it is also necessary for the proper burning of the
fire.
A simple illustration of this is shewn in Fig. 48. The
apparatus consists of a small box which is provided with
two tubes or chimneys as shewn and a glass front.
A candle placed under one of the chimneys represents
a fire. When the candle is lighted convection currents
will circulate in the directions shewn by the arrows.
XIl]
Transmission of Heat
141
This can be seen quite clearly by holding a piece of
smouldering brown paper over
each tube in turn: in one
case the smoke will be drawn
down : in the other it will be
blown up. If the left-hand
chimney be corked up the
flame will burn less brightly
and will be extinguished as
soon as it has exhausted the
oxygen supply in the box.
Fig. 49 illustrates a method
of room or hall ventilation
which depends upon convection currents — as indeed
all systems of "natural ventilation" (as opposed
Fig. 48
Inlet
Flap
outlet
Fig. 49
to forced ventilation by power fans) do. An air inlet
is provided near to the floor and in front of this a
radiator is fixed. The radiator may be hot water,
142 TrauKnu'stiion of Heat [CH.
steam or electric. The air about this radiator expands
and rises and fresh air is drawn in through the inlet.
Outlets are provided round the tops of the walls : the
outlet shewn being a hinged flap which acting like a valve
will only allow air to pass out. An advantage of this
system is that the fresh air is warmed on entering the
room. The circulation of the convection currents will
be demonstrated further by the blackening of the wall
above and behind the radiator at an earlier date than
that of the other walls.
Radiation. Conduction and convection of heat are
processes which require material mediums for the heat
transference. We know however that heat can be
transmitted from one point to another without the aid
of matter : the heat energy which we receive from that
great source of energy the sun is transmitted through
milhons of miles of space. This process of transmission
is called radiation, and it takes place with the velocity
of light, namely 186,000 miles per second. But the
process is not confined to vacuous spaces for radiation
can take place through matter and it can do so without
necessarily raising the temperature of that matter.
To account for these facts the generally adopted
theory is briefly as follows, A hot body is said to be
in a state of vibration. These vibrations are trans-
mitted as such by means of a hypothetical medium
termed the aether of space. This medium is assumed
to be weightless : to pervade all space and the interior
of all matter: and to be highly elastic since it can
transmit the vibrations with an enormous velocity.
The theory fits in with all observed facts and it serves
for the transmission of light as well as of heat.
According to this the fact that heat energy can be
XIl]
Transmission of Heat
143
transmitted through air, or rock salt, without producing
any appreciable increase in temperature, is explained
by the assumption that the heat does not travel as heat
but as vibrations which will be transmitted hke waves
through the aether. When these waves fall upon any
matter they may be reflected ; they may pass through
as waves; they may be absorbed; or some or all of
these possibiUties may take place.
If the matter becomes hotter then we say that some
of the waves are being absorbed and they give up their
energy in the form of heat. If the matter does not
become hotter then the waves are either being reflected
or transmitted.
Reflection and Absorption of Heat. A simple
experiment is illustrated by Fig. 50. Two metal plates
Fig. 50
A and B of the same size and material are placed at
equal distances from a source of heat such as a red hot
iron ball. The plate A is polished whilst B is covered
with a coating of lamp-black or some dull black paint.
From the back of each plate a small tongue of metal
144 TnutsniissioH of Heat \vn.
projects and on each of tliesc tongues a small piece of
yellow phosphorus is placed. In a very short time the
phosphorus behind the black disc will ignite — but the
phosphorus behind the polished disc will not ignite at
all.
This is only one experiment of many which can be
performed to shew that light polished surfaces are good
reflectors of heat (as they are of light) whilst dark and
rough surfaces are bad reflectors but good absorbers.
A fireman's polished brass helmet reflects the heat:
a guardsman's helmet does the same thing. Light
coloured clothing is cooler to wear in summer time than
is dark clothing, since the latter is a bad reflector and
a good absorber of heat.
Transmission and Absorption of Heat. Heat may
be reflected from mirrors in exactly the same way as
light. If an arc lamp be placed at the focus of a concave
mirror the reflected beam — like a searchUght beam —
wiU consist of both light and heat waves. If this beam
falls upon another concave mirror it will be converged
to the focus. The temperature of the air through which
this beam passes will not be appreciably altered : nor
will it be affected at the focus. But a piece of phos-
phorus placed there will ignite immediately. It is only
when the heat waves fall upon some substances (most
substances be it said) that they give up their energy as
heat. Fig. 51 illustrates this.
If such a beam as that mentioned above be allowed
to pass through a strong solution of alum it will be
found that most of the heat waves have been stopped
and the phosphorus placed at the focus of the second
mirror will take longer to ignite if indeed it ignites at all.
The solution of alum will get hot. If a solution of
xii] Transmission of Heat 145
iodine in carbon bisulphide be substituted for the alum
it will be found to stop practically all the light but will
allow the heat to pass through as will be shewn by the
ignition of the phosphorus.
Rock salt will transmit the heat waves readily.
Glass behaves rather remarkably : it will transmit the
heat waves if they proceed from a source at a high
temperature but it stops them if they come from a low
temperature source. It is this property which makes
glass so valuable for greenhouse purposes. The heat
waves from the sun pass through readily enough and
give up their energy to the plants inside ; but after
sunset when the plants are giving out heat instead of
receiving it the glass will not transmit the heat waves
and thus acts as a kind of heat trap.
Focus
Fig. 51
Radiation from different surfaces. Different sur-
faces having the same temperature radiate heat at
different rates. One simple experiment to illustrate
this may be performed with two equal cocoa tins from
which the paper covering has been stripped. One of
the tins should be painted a dull black (a mixture of
lamp-black and turpentine will serve for this purpose)
and through the lid of each a hole should be made large
enough to take a thermometer. The tins are then
p. y. 10
14()
TraiutmisHion of Heat
[CH.
filled with boiling water and it will be found that the
blackened vessel cools much quicker than the bright
vessel. Readings of the two temperatures can be
taken at equal intervals of time and "curves of cooling "
can be plotted.
The usual methods of comparing the radiating
properties of different surfaces are by means of a
thermopile and galvanometer. The two constitute
a sort of electrical thermometer which is much more
sensitive than any expansion thermometer. The prin-
ciple of this thermopile wiU be taken in the electricity
course, but it may be stated here that when the tem-
perature of the exposed thermopile face increases a
current of electricity is set up which causes the needle
of the galvanometer to be deflected. The greater the
temperature the greater will be the current and the
consequent deflection of the needle.
Fig. 52 shews a thermopile being used with a " LesUe
To Galyanometer
Fig. 52
cube " which is simply a metal cube in which >i|jater may
be boiled. The faces of the cube may be treated in
xii] Transmission of Heat 147
different ways : or they may be made of different
metals or covered with different materials. In this
way a simple method is provided for heating a number
of different surfaces to the same temperature. The
thermopile is placed the same distance away from each
face in turn and the permanent deflection of the
galvanometer needle gives a measure of the rate at
which the thermopile receives heat from each face.
If it receives more heat per second in one case than in
another then clearly its temperature will rise to a
higher degree.
It will be found in general that pohshed surfaces do
not radiate heat so well as dull surfaces and that light
coloured surfaces are worse radiators than dark surfaces.
A polished metal teapot does not require a "tea-
cosy" : a dirty one does, for two reasons.
The "vacuum" flasks so largely used in these days
depend upon this for their property of retaining the
temperature of any liquids placed in them. They con-
sist of a double walled glass vessel and the space
between the two walls has the air driven out of it
whilst a small quantity of quicksilver is vaporised
inside. The inter- wall space is then sealed and the
quicksilver condenses on the inside of the walls —
forming a complete mirror coating. Thus the flask
does not absorb the heat readily and what it does
absorb it does not radiate readily. The absence of
air from the space between the two walls of the flask
prevents convection currents, but it is the non-radiating
property of the silvered surface which is the main
cause of the insulating property of the flask.
Flame radiation. The amount of radiation from
a flame depends very much upon its nature. The
10—2
148 Transmission of Heat [CH. xii
luminosity of a candle flame depends upon the presence
of solid particles of carbon within it, and the same
appUes to the old-fashioned batswing gas flame. If
the gas of a burner be mixed with air before ignition
— as in the case of a Bunsen burner or a gas stove or
the burner of an incandescent gas — the soUd particles
of carbon do not exist in it for any appreciable time
and very little light or heat is radiated. At the same
time this flame is hotter than the batswing flame and
can raise the temperature of substances to a greater
degree. A gas mantle placed over such a flame becomes
hotter and gives out more light and radiant heat than
it would if it were placed over the batswing flame.
Formation of Dew. After sunset the earth radiates
some of the heat it has received during the day, and
a fall of temperature results. If the night be cloudy
then the clouds reflect and radiate heat back again
so that the fall in temperature is not very great. If
the night be clear the heat is radiated into space and
the temperature falls much more.
The earth thus becomes cooled and often to a tem-
perature below the dew-point (see p. 130). Dew is
generally deposited upon blades of grass whilst it is not
noticeable upon bare earth or stones because the blades
of grass are excellent radiators and become very cold
and are also bad conductors so that they do not
receive any heat from the earth by conduction.
Straw is an excellent radiator and a bad conductor
and because of this it is possible to freeze water during
the night in hot regions of India and other places by
putting some water in a shallow vessel and standing it
upon a heap of straw.
CHAPTER XIII
THERMODYNAMICS
In Chapters IV and V we pointed out that heat
might be considered as a form of energy, and we shewed
some of the methods by means of which other forms
of energy could be changed into the form which we
call heat. The most primitive method of generating
sufficient heat to kindle a fire consists in causing friction
to be developed rapidly between two dry pieces of wood
— preferably and most easily by bending one piece into
the form of a rough brace and using one end as a "bit"
in the vain endeavour to bore a hole in the other piece.
The operator will not be successful in boring but he
will soon find that the "bit" will ignite. The energy
which is converted into heat energy is the mechanical
energy of the operator.
Experiments have been performed by means of
which the relationship between the amount of mechani-
cal work expended and the quantity of heat produced
has been ascertained.
Mechanical Equivalent of Heat. The amount of
mechanical work which must be done so that when it
is all converted into heat it will produce one unit of
heat is called the mechanical equivalent of heat. Many
1 50 Thei'mo-Df/namics [CH.
different kinds of experiments have been performed
by various experimenters and the results obtained are
all in close agreement.
On the British system of units it has been found
that in order to produce one British thermal unit of heat
by the expenditure of mechanical energy, 778 foot-lbs.
of work must be done.
On the metric system 4-2 joules (or 4-2 x 10' ergs)
must be done in order to generate 1 calorie.
Method of Determination. Count Rumford and
Dr Joule were the experimentalists whose names are
most generally associated with the determination of
the mechanical equivalent of heat. Rumford's experi-
ments were performed by boring cannon with sharp
and blunt borers. In the latter case more work had
to be done in the boring operation and proportionately
more heat was developed. Dr Joule's apparatus con-
sisted of a paddle arrangement which he rotated in
a special calorimeter containing a known mass of water
at a known temperature. The paddle wheel was made
to rotate at a uniform rate by means of an arrangement
of falling weights. In order to prevent the water from
turning round with the paddle, some fixed arms pro-
jected inwards from the wall of the calorimeter. The
weights were allowed to fall through a known distance :
they were then quickly wound up again without turning
the paddle wheel and allowed to fall again: and this
was repeated until an easily measurable rise of tempera-
ture was produced iii the water. The total work done
by the falling weights was then calculated, and the
amount of heat generated was determined by the
product of the total equivalent weight of the water and
calorimeter and paddles and the increase in temperature.
XIII
Thermo- Dynmnics
151
From this the work done per unit of heat generated was
readily ascertained.
A favourite laboratory method of malting this
determination is that in which the apparatus shewn
in Fig. 53 is used.
Fig. 53
The "calorimeter" consists of two brass cones Cj
and O2 which can revolve on one another about a vertical
axis. If Oj is fixed C^ can be turned round by means
152 Thermo- hiiiin III irs [ch.
of a weiglit W on a piece of string which is fixed to a
large wooden pulley P at the top of the apparatus. On
the other hand if Cj be rotated in the opposite direction
to that in which the weight would rotate C^ it can be
seen that at a certain speed of rotation the tendency of
the weight to fall could be exactly balanced. If the
speed of Cj were increased then W would rise : if it were
decreased W would fall. Thus if we rotate Cj at such
a speed that W remains stationary it follows that the
work which we do per revolution must be exactly the
same as if the weight had fallen through such a distance
that it turned C^ through one revolution. And it there-
fore follows that the work done per revolution when we
keep W stationary is given by the product of W and
the circumference of the pulley P.
This is the method by means of which the work
which is done in overcoming the friction of the cones
is determined. The outer cone Cj is held by two pins
projecting from an insulating base B. This in turn is
fixed to a vertical spindle 8 which can be rotated by
means of a belt DB which passes round a small driving
pulley DP. In order to make it easy to count the total
number of revolutions there is a worm thread T on the
spindle and this engages with a toothed wheel R having,
say, 100 teeth, every ten of which are marked. A fixed
pointer on the supporting arm of the toothed wheel
serves as recorder. The inner cone Cg is fixed to the
top pulley by means of two projecting pins.
The cones (both of them) are weighed and their
w^ater equivalent is determined. The inner cone is
then partially filled with mercury and the whole weighed
again in order to get the weight of mercury. The water
equivalent of the mercury is then calculated and the
xiii] Thermo- Dynamics 153
sum of the two water equivalents gives the total water
equivalent of the cones and the mercury.
Mercury is used because it has a small specific heat
and is a good conductor. Thus we can get a greater
rise in temperature than we should get if we used water :
and in this way we reduce the possible errors of tempera-
ture reading.
The temperature of the mercury is taken, and then
the spindle is rotated at such a speed that W remains
steady. This requires a little experience and some
prehminary trials are necessary.
When the temperature has risen through a reason-
able and readable range the rotation is stopped and
the final temperature and the total number of revolu-
tions are determined.
The mechanical equivalent is determined as follows :
Heat : Mass of the cones = M^ lbs. Specific heat
of cones = 8^.
Water equivalent of cones = M^ x 8^ lbs.
Mass of mercury = Jf„j lbs. Specific heat of
mercury = 8^-
Therefore water equivalent of mercury = M^ x 8^
lbs.
Therefore total water equivalent of cones and mer-
cury = M^8c + M^8^ = Jf lbs.
Original temperature of mercury = 1°!^.
Final temperature of mercury = ^2° ^•
Therefore units generated = M {t^ — t-^) b.th.u.
= H units.
Work : Weight on the pulley string = W lbs.
Circumference of pulley = G feet = ttD feet, where
D = diameter in feet.
Number of revolutions = N.
\i>4 r/iniHO-JJi/namics [en.
Therefore total work done = WON foot-lbs. =- J
foot -lbs.
Relationship : Since H units of heat are produced
by J foot-lbs, of work therefore 1 unit of heat will be
produced by rj foot-lbs.
Therefore the mechanical equivalent of heat = ^
11
foot-lbs, per b.th.it.
Fundamental principle of the Heat Engine. Just as
mechanical work may be converted into heat so by
proper arrangements heat may be converted into
mechanical work. Any device by means of which
this may be done is called a heat engine, and it would
be well if we consider at this stage how such an engine
does work at the expense of heat energy.
The thoughtful student might argue that in the case
of a steam engine although heat energy is necessary to
produce the steam which forces the piston along the
cylinder yet the steam comes out of the exhaust as
steam and has not given out any heat except that
necessary to warm up the piston and cylinder in the
first instance. Such argument however would be
wrong, for it can easily be shewn that heat is given out
by the steam as it expands in the cylinder, anxi the
energy of the steam engine is represented by the energy
given out during this expansion.
Let us imagine that we have a tall cylinder and that
it is fitted with a piston which when loaded with a
number of weights sinks do^vn into the cylinder and
so compresses the air in it. If we then remove the
weights one by one the air will expand and will
do work in raising up the piston and the remaining
xiii] Thermo- Dynamics 155
weights. Now if the weights be removed in sufficiently
quick succession it will be found that the air is cooled
by its expansion. We therefore conclude that some of
the heat energy of the air has been converted into the
mechanical work necessary to lift the weights, and
therefore the temperature of the air must be reduced.
On the other hand if the air be compressed it will be
found that its temperature rises and we conclude that
the mechanical work done in compression is converted
into heat. Probably all our readers know how hot the
end of a bicycle pump gets after a few rapid strokes of
the piston.
But — to return to our tall cylinder with its weighted
piston — after we have compressed the air and so heated
it, if we allow it to cool down again to the temperature
of the surrounding air and then allow the piston to rise
once more we shall again find that the air is cooled.
The point here aimed at is that though we may produce
heat by compression yet if we allow it to disappear we
shall nevertheless take heat away again on expansion.
Work must be done on the air in compressing it : that
work is changed to heat and the temperature of the air
rises. Work must be done by the air in expanding and
it is done at the expense of some of the heat energy of
the air which is thereby cooled.
The reader may remember that in our chapter on
specific heat we stated that the specific heat of a gas is
greater if the volume of the gas be allowed to change
as it is heated than it is if the volume of the gas be
kept constant during heating. The reason for this is
now obvious. If when heating a gas it expands it
must be doing work. The gas need not be actually
pushing a piston along a cylinder, but as it expands
150 Tlicnno-Djimtmim [CH.
it must be pushing air away from it and therefore must
be doing mechanical work. The energy for this must
come from somewhere : it comes from the heat energy
of the air and so the air would be cooled. Therefore
to keep the air up to its temperature more heat would
have to be given to it than would have been necessary
had the air not been expanding.
The reader will be able to see that the difference
between the amount of heat necessary to raise the
temperature of a given mass of gas through a certain
range without any change in volume, and that necessary
to produce the same temperature change when the gas
is expanding, will represent the amount of energy which
is changed from heat energy to mechanical energy.
In the case of the steam engine if we measure the
quantity of heat energy in each lb. of steam as it enters
the cylinder and again as it leaves, the difference will
represent the amount of energy which each lb. of steam
gives out to the engine as mechanical energy. If we
know the number of lbs. of steam per minute which are
passing through (an easily determined quantity), then
we have at once the means of calculating the mechanical
energy given per minute by the steam, and from that
the horse-power. This, of course, does not give the
horse -power which the engine will yield : that wiU
depend upon the efficiency of the engine.
Effect of compression and expansion on saturated
steam. We saw on page 124 that when a space was
saturated a change of volume did not affect the pressure
if the temperature remained constant. We are now in
a position to see that unless the change in volume is
effected very slowly indeed the temperature will be
increased on compression and this increase might be
xiii] Thermo- Dynamics 157
sufficient to convert the space into a non-saturated one
(or a superheated one). Indeed in the case of steam
this is the case, for if saturated steam be suddenly-
compressed in a space from which no heat can escape
the consequent rise in temperature is such that the
space becomes superheated — that is to say instead of
the compression producing condensation of the steam
in the cyUnder as we should expect it to do from
Dalton's experiments on saturated spaces (page 124),
enough heat is developed to raise the temperature
sufficiently to render the space hot enough to be able
to hold even more water vapour.
On the other hand if saturated steam be allowed to
expand, doing the full amount of work of which it is
capable during the expansion, it loses so much heat
that, notwithstanding the increased volume, condensa-
tion takes place.
When this happens in the cyhnder of an engine the
condensed water accumulates. This is called priming.
In all steam engines working expansively means are
taken to prevent this condensation — such, for example,
as surrounding the cylinder with a steam jacket.
If superheated or non-saturated steam be used
then, of course, this condensation wiU not occur if the
steam is sufficiently far from saturation.
Isothermal and Adiabatic expansion. If the volume
of a given mass of gas be changed without any change
of temperature it is said to be changed isothermally.
From what we have seen above it follows that such
isothermal change of volume can only be produced
provided that heat is taken from or given to the gas.
As it is compressed then heat must be taken from the
gas in order that its temperature shall not rise. As it
158 Thermo- DjfnamicM [CH.
is expanded heat must be given to it to prevent the
temperature from falling. Boyle's law, for example,
is only true for an isothermal change : it states that
the temperature must be kept constant. The curve
which we plotted to shew tlie relationship between
pressure and volume of a gas at constant temperature
is called an isothermal curve connecting pressure and
volume.
If, on the other hand, the gas be contained in some
vessel which will not permit it to receive or lose heat,
then as it is compressed its temperature will rise and
as it expands its temperature will fall but the quantity
of heat will remain constant. Such a change is said
to be adiabatic or isentropic. Boyle's law is not true
for adiabatic expansion or compression. On compres-
sion the temperature will be raised and therefore the
gas will occupy a greater volume at a given pressure.
On expansion the gas wiU be cooled and the volume will
be less than it would be at a given pressure. Fig. 54
shews the difference : the curve IBL is an isothermal
or Boyle's law curve shewing the relationship between
pressure and volume : the curve ABC is the adiabatic
curve for the same mass of gas. The point B is the
starting point and if the gas be compressed adia-
batically its volume wiU not fall as much as it would
if compressed isothermally, and vice versa. Thus the
adiabatic curve is steeper than the isothermal curve.
For the same reasons it follows that if we compress
a gas adiabatically the mean pressure necessary to
produce a given change in volume will be greater than
that necessary to produce the same change in volume
if the gas be compressed isothermally. Therefore it
follows that more work must be done to compress
XIIl]
Thermo- Dfpiamics
159
a gas adiabatically than isothermally and more work
will be given out by a gas expanding adiabatically
than isothermally.
The Indicator diagram. If we can plot a curve which
shews the pressure on a piston at each position of its
motion along a cylinder we can then get the mean
pressure from the curve. If we know this mean pressure
in lbs. per square inch and the area of cross section of
the piston and the length of its stroke in the cylinder
Volume
Fig. 54
we can calculate the total work done upon it per stroke.
If, further, we know the number of strokes which it
makes per minute we can determine the rate of working
or the horse -power yielded by the steam.
Such a curve shewing the relationship between
pressure and position of piston is called an indicator
diagram.
If the pressure on the piston were constant through
the full length of the stroke and then dropped suddenly
to zero at the end, the diagram would be like that
160
Thermo- Dynamics
[CH.
shewn in Fig. 55. The height OA represents the steam
pressure on the piston and the position of the piston
in the cyUnder is represented by such distances as
OM, OC.
The point C represents the end of the stroke. As
the piston returns again to 0 we are assuming that
the pressure upon it is zero and when it reaches O
the pressure suddenly becomes OA again.
i I I i I I I I
I ! I I I I I I
I ■ I I I I I I
! > I I I ' I ■
I nI I 1 B
o
M
Position of Piston along Cylinder
Fig. 55
If such conditions were possible and such an in-
dicator diagram were obtained the horse-power of the
engine concerned could be readily determined.
Let A represent the area of the piston in square
inches.
Let P represent the average pressure* upon the
* By this is meant the net average pressure or the average
difference of pressure on each side of the piston.
XIIl]
Thermo-Dynamics
161
piston — both journeys along the cyhnder being con-
sidered. In this case the pressure is constant and is
represented by OA on our diagram. The return
journey pressure is zero in this case.
Then P y, A = total force in lbs. on the piston.
Let L = length of stroke in feet.
Then PAL = force x distance = work in foot-lbs.
for each journey of piston to and fro.
If iV^ = no. of to and fro movements per minute.
Then PLAN = foot-lbs. per minute.
Fig. 56 represents more nearly the actual relation-
ship between the pressure and the position of the piston.
Atmospheric
line of pressure
Position of Piston along cylinder
Fig. 56
The portion of the diagram AB indicates that for the
first part of the stroke the pressure is constant (practi-
cally, in fact, the boiler pressure). At the point B the
steam port'is shut and the steam expands as the piston
P.Y. 11
162 Thermo- Dynamics [ch. xiii
continues its motion, but the pressure falls as shewn by
the curve BC. At the point C the exhaust port is
opened and the pressure falls rapidly to atmospheric
pressure shewn at D which is the extremity of the stroke.
The piston then returns and when back again at the
point E the exhaust port is closed so that the small
amount of steam left in the cylinder shall act as a
cushion to assist the return of the piston. This steam
becomes compressed as the piston approaches 0 and
the pressure rises as shewn by the curve EF. When
the piston reaches O the steam port is opened again
and the pressure rises at once to the point A.
In order to find the indicated horse-power with the
aid of this diagram it is clear that we shall need to find
the average pressure on the cyhnder during the complete
to and fro motion of the piston. The net average
pressure will be the difference between the average
outward pressure and the average return pressure. On
the outward journey when the piston is at L the pressure
is LN, on the return journey the pressure is LM at the
same position. Therefore the net or useful pressure is
represented by the difference, namely MN. It will be
seen that the net average pressure per complete cycle
will be given by the average of such lengths as FA, QR,
MN. Thus if a sufficient number of such ordinates be
drawn at equal distances apart and their mean length
determined — in terms of the pressure scale — we shall
get the net average pressure at once.
If the engine w^re to exhaust into a condenser in
which the pressure was less than the atmospheric
pressure then the return part of the diagram DE would
fall below the position shewn : in which case it is clear
that the net mean pressure would be greater.
INDEX
Absolute scale of temperature 90
Absolute zero 92
Absorption of heat 143-4
Adiabatic expansion 157
Advantages of expansion 76
Airships 46
Alcohol thermometer 68, 70
Apparent expansion of liquid 81
Archimedes, Principle of 24
Atmospheric pressure 37, 40
Balloons 46
Barometer 41; standard 42
Boiler test 31
Boiling point 64, 115
Boyle's Law and vapour pressure
123
Boyle's Law for gases 42
British Thermal Unit 96
Buoyancy 22
Calorie 96
Calorific value of fuels 102
Calorimeter 100; Darling's 103
Capillarity 32
Celsius 65
Centigrade scale 65
Charles' Law 87
Classification of matter 8
Clinical thermometer 71
Coeificient of expansion of gas 86 ;
of liquid 82; of solid 73
Compensation for expansion 79
Compression of saturated steam 156
Condensation 1 15
Conduction of heat 133
Conductivity, thermal 134
Conservation of energy 54
Convection 137, 139
Conversion of temperature scales
68
Cubical expansion 80
Dalton's Law 122
Darling's calorimeter 103
Densities, table of 11
Density 9 ; relative 25
Dew, formation of 148
Dew point 130
Diagram indicator 159
Diffusion 34
Displacement 25
Dyne 50
Elasticity 12
Energy 52; conservation of 54;
kinetic 52; potential 52
Erg 50
Evaporation 115, 120
Expansion 72-94; of saturated
steam 156
Fahrenheit scale 65
Feed- water pump 31
Fixed points of temperature 63
Flame radiation 147
Floating bodies 23, 46
Foot-pound 48
164
Imlesc
Foot-poundal 49
Force 2, 48; units of 49
Freezing point 63
Freezing points of liquids 108
Fusion 107
Gases, ex{)ansian of 8fi
Gases, properties of 37-46
Gravitation, force of 2
Gridiron pendulum 79
Heat and temperature 60
Heat engine, principle of 154
Heat, latent 126; sensible 126;
specific 97; total 126; unit
of 96
Heat, mechanical equivalent of
149
Hooke's law 13
Horse-power 56
Horse-power of steam engine
160
Hot water circulation 139
Humidity 129
Hydrometers 28
Hygrometers 131
Indicator diagram 159
Inertia 5
Isentropic expansion 158
Isothermal expansion 157
Joule 50, 150
Joule's experiment 150
Kilowatt 56
Kinetic energy 56
Kinetic theory 7, 91
Latent heat of fusion 109; of
vaporisation 125
Leslie cube 146
Limits of elasticity 12
Liquid, expansion of 81
Liquid pressure 16, 24; pro-
perties 15
Mass 4; units of 51
Matter, classification of 8; inde-
structibility of • 2 ; structure of
7 ; properties of 1
Maximum and minimum thermo-
meters 70
Maximum density of water 84
Mechanical equivalent of heat 149
Melting point 107 ; effect of
pressure on 113
Modulus of elasticity 7
Motion 3; energy of 62
Potential energy 62
Power 54
Pressure and boiling point 63,
116; and melting point 113;
in liquids 16, 24; of gases 38
Principle of Archimedes 24; con-
servation of energy 54
Pumps 29
Pyrometer 69
Radiation of heat 142
Reaumur temperature scale 66
Reflexion of heat 143
Relative density 26
Rigidity 9
Safety lamp 136
Saturated steam 119, 129
Saturation 120
Scales of temperature 66
Sensible heat 126
Solidification 106
Solidification, change of volume
on 111
Solids, properties of 11
Solution 113
Specific gravity 25; bottle 28
Specific heat 97 ; of gases 105
Index
165
States of matter 1
Steam, temperature and pressure
of 64, 116; latent heat 125;
total heat 126
Strain 12
Stress 13
Structure of matter 7
Superficial expansion 79
Superheated space 157
Surface tension 33
Tables — calorific values 105; co-
efficients of expansion 76 ; den-
sities 1 1 ; latent heats 109 ;
melting points 106; specific
heats 98; volume and temper-
ature of water 85
Temperature 59; absolute zero
of 91; absolute scale of 92;
fixed points 63; scales 65
Temperature and pressure of
steam 64, 116
Tension, surface 33
Thermometers 61; self -registering
70
Thermopile 146
Torsion 13
Total heat of steam 126
Transmissi9n of heat 133
Unit of force 48; of heat 96;
of power 55; of work 49
Vacuum flask 147
Vapori sation 115
Vapour pressure 122; and tem-
perature 125
Ventilation 140
Viscosity 35
Volumenometer It)
Voluminal expansion 80
Water equivalent 99
Water, expansion of 82
Watt 56
Weight 2
Weight of air 4
Work 48; units of 49
Young's modulus of elasticity 7
CAMBRIDGE: PRINTED BY J. B. PEACE, M.A., AT THE UNIVERSITY PRESS
I
THE CAMBRIDGE TECHNICAL SERIES
General Editor: P. ABBOTT, B.A.,
HEAD OF THE MATHEMATICAL DEPARTMENT, THE POLYTECHNIC,
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